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Biblioteca

MARC Lista (tabellare)
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
Autore Braun Philipp
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (123 pages)
Disciplina 003.71
Collana SpringerBriefs in Mathematics
Soggetto topico Estabilitat
Equacions diferencials
Lyapunov stability
Differential equations
Soggetto genere / forma Llibres electrònics
ISBN 3-030-76317-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910492152103321
Braun Philipp  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
Autore Braun Philipp
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (123 pages)
Disciplina 003.71
Collana SpringerBriefs in Mathematics
Soggetto topico Estabilitat
Equacions diferencials
Lyapunov stability
Differential equations
Soggetto genere / forma Llibres electrònics
ISBN 3-030-76317-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466391503316
Braun Philipp  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Applying Power Series to Differential Equations [[electronic resource] ] : An Exploration through Questions and Projects / / by James Sochacki, Anthony Tongen
Applying Power Series to Differential Equations [[electronic resource] ] : An Exploration through Questions and Projects / / by James Sochacki, Anthony Tongen
Autore Sochacki James
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (XII, 217 p. 45 illus., 36 illus. in color.)
Disciplina 515.35
Collana Problem Books in Mathematics
Soggetto topico Differential equations
Sequences (Mathematics)
Dynamics
Nonlinear theories
Algebraic fields
Polynomials
Differential Equations
Sequences, Series, Summability
Applied Dynamical Systems
Field Theory and Polynomials
Equacions diferencials
Successions (Matemàtica)
Dinàmica
Teories no lineals
Soggetto genere / forma Llibres electrònics
ISBN 3-031-24587-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Introduction: The Linear ODE: x′ = bx + c -- Chapter 2. Egg 1: The Quadratic ODE: x′ = ax2 + bx + c -- Chapter 3. Egg 2: The First Order Exponent ODE: x′ = xr -- Chapter 4. Egg 3: The First Order Sine ODE: x′ = sin x -- Chapter 5. Egg 4: The Second Order Exponent ODE: x′′ = −xr -- Chapter 6. Egg 5: The Second Order Sine ODE - The Single Pendulum -- Chapter 7. Egg 6: Newton’s Method and the Steepest Descent Method -- Chapter 8. Egg 7: Determining Power Series for Functions through ODEs -- Chapter 9. Egg 8: The Periodic Planar ODE: x′ = −y + ax2 + bxy + cy2 ; y′ = x + dx2 + exy + fy2 -- Chapter 10. Egg 9: The Complex Planar Quadratic ODE: z′ = az2 + bz + c -- Chapter 11. Egg 10: Newton’s N-Body Problem -- Chapter 12. Egg 11: ODEs and Conservation Laws -- Chapter 13. Egg 12: Delay Differential Equations -- Chapter 14. An Overview of Our Dozen ODEs -- Chapter 15. Appendix 1. A Review of Maclaurin Polynomials and Power Series -- Chapter 16. Appendix 2. The Dog Rabbit Chasing Problem -- Chapter 17. Appendix 3. A PDE Example: Burgers’ Equation -- References.
Record Nr. UNISA-996518463403316
Sochacki James  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Applying Power Series to Differential Equations [[electronic resource] ] : An Exploration through Questions and Projects / / by James Sochacki, Anthony Tongen
Applying Power Series to Differential Equations [[electronic resource] ] : An Exploration through Questions and Projects / / by James Sochacki, Anthony Tongen
Autore Sochacki James
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (XII, 217 p. 45 illus., 36 illus. in color.)
Disciplina 515.35
Collana Problem Books in Mathematics
Soggetto topico Differential equations
Sequences (Mathematics)
Dynamics
Nonlinear theories
Algebraic fields
Polynomials
Differential Equations
Sequences, Series, Summability
Applied Dynamical Systems
Field Theory and Polynomials
Equacions diferencials
Successions (Matemàtica)
Dinàmica
Teories no lineals
Soggetto genere / forma Llibres electrònics
ISBN 3-031-24587-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Introduction: The Linear ODE: x′ = bx + c -- Chapter 2. Egg 1: The Quadratic ODE: x′ = ax2 + bx + c -- Chapter 3. Egg 2: The First Order Exponent ODE: x′ = xr -- Chapter 4. Egg 3: The First Order Sine ODE: x′ = sin x -- Chapter 5. Egg 4: The Second Order Exponent ODE: x′′ = −xr -- Chapter 6. Egg 5: The Second Order Sine ODE - The Single Pendulum -- Chapter 7. Egg 6: Newton’s Method and the Steepest Descent Method -- Chapter 8. Egg 7: Determining Power Series for Functions through ODEs -- Chapter 9. Egg 8: The Periodic Planar ODE: x′ = −y + ax2 + bxy + cy2 ; y′ = x + dx2 + exy + fy2 -- Chapter 10. Egg 9: The Complex Planar Quadratic ODE: z′ = az2 + bz + c -- Chapter 11. Egg 10: Newton’s N-Body Problem -- Chapter 12. Egg 11: ODEs and Conservation Laws -- Chapter 13. Egg 12: Delay Differential Equations -- Chapter 14. An Overview of Our Dozen ODEs -- Chapter 15. Appendix 1. A Review of Maclaurin Polynomials and Power Series -- Chapter 16. Appendix 2. The Dog Rabbit Chasing Problem -- Chapter 17. Appendix 3. A PDE Example: Burgers’ Equation -- References.
Record Nr. UNINA-9910682548903321
Sochacki James  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Autore Karpfinger Christian
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2022]
Descrizione fisica 1 online resource (1015 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Calculus
Differential equations
Àlgebra lineal
Càlcul
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783662654583
9783662654576
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Speech, Symbols and Sets -- 1.1 Speech Patterns and Symbols in Mathematics -- 1.1.1 Junctors -- 1.1.2 Quantifiers -- 1.2 Summation and Product Symbol -- 1.3 Powers and Roots -- 1.4 Symbols of Set Theory -- 1.5 Exercises -- 2 The Natural Numbers, Integers and Rational Numbers -- 2.1 The Natural Numbers -- 2.2 The Integers -- 2.3 The Rational Numbers -- 2.4 Exercises -- 3 The Real Numbers -- 3.1 Basics -- 3.2 Real Intervals -- 3.3 The Absolute Value of a Real Number -- 3.4 n-th Roots -- 3.5 Solving Equations and Inequalities -- 3.6 Maximum, Minimum, Supremum and Infimum -- 3.7 Exercises -- 4 Machine Numbers -- 4.1 b-adic Representation of Real Numbers -- 4.2 Floating Point Numbers -- 4.2.1 Machine Numbers -- 4.2.2 Machine Epsilon, Rounding and Floating Point Arithmetic -- 4.2.3 Loss of Significance -- 4.3 Exercises -- 5 Polynomials -- 5.1 Polynomials: Multiplication and Division -- 5.2 Factorization of Polynomials -- 5.3 Evaluating Polynomials -- 5.4 Partial Fraction Decomposition -- 5.5 Exercises -- 6 Trigonometric Functions -- 6.1 Sine and Cosine -- 6.2 Tangent and Cotangent -- 6.3 The Inverse Functions of the Trigonometric Functions -- 6.4 Exercises -- 7 Complex Numbers: Cartesian Coordinates -- 7.1 Construction of C -- 7.2 The Imaginary Unit and Other Terms -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Exercises -- 8 Complex Numbers: Polar Coordinates -- 8.1 The Polar Representation -- 8.2 Applications of the Polar Representation -- 8.3 Exercises -- 9 Linear Systems of Equations -- 9.1 The Gaussian Elimination Method -- 9.2 The Rank of a Matrix -- 9.3 Homogeneous Linear Systems of Equations -- 9.4 Exercises -- 10 Calculating with Matrices -- 10.1 Definition of Matrices and Some Special Matrices.
10.2 Arithmetic Operations -- 10.3 Inverting Matrices -- 10.4 Calculation Rules -- 10.5 Exercises -- 11 LR-Decomposition of a Matrix -- 11.1 Motivation -- 11.2 The LR-Decomposition: Simplified Variant -- 11.3 The LR-Decomposition: General Variant -- 11.4 The LR-Decomposition-with Column Pivot Search -- 11.5 Exercises -- 12 The Determinant -- 12.1 Definition of the Determinant -- 12.2 Calculation of the Determinant -- 12.3 Applications of the Determinant -- 12.4 Exercises -- 13 Vector Spaces -- 13.1 Definition and Important Examples -- 13.2 Subspaces -- 13.3 Exercises -- 14 Generating Systems and Linear (In)Dependence -- 14.1 Linear Combinations -- 14.2 The Span of X -- 14.3 Linear (In)Dependence -- 14.4 Exercises -- 15 Bases of Vector Spaces -- 15.1 Bases -- 15.2 Applications to Matrices and Systems of Linear Equations -- 15.3 Exercises -- 16 Orthogonality I -- 16.1 Scalar Products -- 16.2 Length, Distance, Angle and Orthogonality -- 16.3 Orthonormal Bases -- 16.4 Orthogonal Decomposition and Linear Combination with Respect to an ONB -- 16.5 Orthogonal Matrices -- 16.6 Exercises -- 17 Orthogonality II -- 17.1 The Orthonormalization Method of Gram and Schmidt -- 17.2 The Vector Product and the (Scalar) Triple Product -- 17.3 The Orthogonal Projection -- 17.4 Exercises -- 18 The Linear Equalization Problem -- 18.1 The Linear Equalization Problem and Its Solution -- 18.2 The Orthogonal Projection -- 18.3 Solution of an Over-Determined Linear System of Equations -- 18.4 The Method of Least Squares -- 18.5 Exercises -- 19 The QR-Decomposition of a Matrix -- 19.1 Full and Reduced QR-Decomposition -- 19.2 Construction of the QR-Decomposition -- 19.3 Applications of the QR-Decomposition -- 19.3.1 Solving a System of Linear Equations -- 19.3.2 Solving the Linear Equalization Problem -- 19.4 Exercises -- 20 Sequences -- 20.1 Terms.
20.2 Convergence and Divergence of Sequences -- 20.3 Exercises -- 21 Calculation of Limits of Sequences -- 21.1 Determining Limits of Explicit Sequences -- 21.2 Determining Limits of Recursive Sequences -- 21.3 Exercises -- 22 Series -- 22.1 Definition and Examples -- 22.2 Convergence Criteria -- 22.3 Exercises -- 23 Mappings -- 23.1 Terms and Examples -- 23.2 Composition, Injective, Surjective, Bijective -- 23.3 The Inverse Mapping -- 23.4 Bounded and Monotone Functions -- 23.5 Exercises -- 24 Power Series -- 24.1 The Domain of Convergence of Real Power Series -- 24.2 The Domain of Convergence of Complex Power Series -- 24.3 The Exponential and the Logarithmic Function -- 24.4 The Hyperbolic Functions -- 24.5 Exercises -- 25 Limits and Continuity -- 25.1 Limits of Functions -- 25.2 Asymptotes of Functions -- 25.3 Continuity -- 25.4 Important Theorems about Continuous Functions -- 25.5 The Bisection Method -- 25.6 Exercises -- 26 Differentiation -- 26.1 The Derivative and the Derivative Function -- 26.2 Derivation Rules -- 26.3 Numerical Differentiation -- 26.4 Exercises -- 27 Applications of Differential Calculus I -- 27.1 Monotonicity -- 27.2 Local and Global Extrema -- 27.3 Determination of Extrema and Extremal Points -- 27.4 Convexity -- 27.5 The Rule of L'Hospital -- 27.6 Exercises -- 28 Applications of Differential Calculus II -- 28.1 The Newton Method -- 28.2 Taylor Expansion -- 28.3 Remainder Estimates -- 28.4 Determination of Taylor Series -- 28.5 Exercises -- 29 Polynomial and Spline Interpolation -- 29.1 Polynomial Interpolation -- 29.2 Construction of Cubic Splines -- 29.3 Exercises -- 30 Integration I -- 30.1 The Definite Integral -- 30.2 The Indefinite Integral -- 30.3 Exercises -- 31 Integration II -- 31.1 Integration of Rational Functions -- 31.2 Rational Functions in Sine and Cosine -- 31.3 Numerical Integration.
31.4 Volumes and Surfaces of Solids of Revolution -- 31.5 Exercises -- 32 Improper Integrals -- 32.1 Calculation of Improper Integrals -- 32.2 The Comparison Test for Improper Integrals -- 32.3 Exercises -- 33 Separable and Linear Differential Equations of First Order -- 33.1 First Differential Equations -- 33.2 Separable Differential Equations -- 33.2.1 The Procedure for Solving a Separable Differential Equation -- 33.2.2 Initial Value Problems -- 33.3 The Linear Differential Equation of First Order -- 33.4 Exercises -- 34 Linear Differential Equations with Constant Coefficients -- 34.1 Homogeneous Linear Differential Equations with Constant Coefficients -- 34.2 Inhomogeneous Linear Differential Equations with Constant Coefficients -- 34.2.1 Variation of Parameters -- 34.2.2 Approach of the Right-Hand Side Type -- 34.3 Exercises -- 35 Some Special Types of Differential Equations -- 35.1 The Homogeneous Differential Equation -- 35.2 The Euler Differential Equation -- 35.3 Bernoulli's Differential Equation -- 35.4 The Riccati Differential Equation -- 35.5 The Power Series Approach -- 35.6 Exercises -- 36 Numerics of Ordinary Differential Equations I -- 36.1 First Procedure -- 36.2 Runge-Kutta Method -- 36.3 Multistep Methods -- 36.4 Exercises -- 37 Linear Mappings and Transformation Matrices -- 37.1 Definitions and Examples -- 37.2 Image, Kernel and the Dimensional Formula -- 37.3 Coordinate Vectors -- 37.4 Transformation Matrices -- 37.5 Exercises -- 38 Base Transformation -- 38.1 The Tansformation Matrix of the Composition of Linear Mappings -- 38.2 Base Transformation -- 38.3 The Two Methods for Determining Transformation Matrices -- 38.4 Exercises -- 39 Diagonalization: Eigenvalues and Eigenvectors -- 39.1 Eigenvalues and Eigenvectors of Matrices -- 39.2 Diagonalizing Matrices -- 39.3 The Characteristic Polynomial of a Matrix.
39.4 Diagonalization of Real Symmetric Matrices -- 39.5 Exercises -- 40 Numerical Calculation of Eigenvalues and Eigenvectors -- 40.1 Gerschgorin Circles -- 40.2 Vector Iteration -- 40.3 The Jacobian Method -- 40.4 The QR-Method -- 40.5 Exercises -- 41 Quadrics -- 41.1 Terms and First Examples -- 41.2 Transformation to Normal Form -- 41.3 Exercises -- 42 Schur Decomposition and Singular Value Decomposition -- 42.1 The Schur Decomposition -- 42.2 Calculation of the Schur Decomposition -- 42.3 Singular Value Decomposition -- 42.4 Determination of the Singular Value Decomposition -- 42.5 Exercises -- 43 The Jordan Normal Form I -- 43.1 Existence of the Jordan Normal Form -- 43.2 Generalized Eigenspaces -- 43.3 Exercises -- 44 The Jordan Normal Form II -- 44.1 Construction of a Jordan Base -- 44.2 Number and Size of Jordan Boxes -- 44.3 Exercises -- 45 Definiteness and Matrix Norms -- 45.1 Definiteness of Matrices -- 45.2 Matrix Norms -- 45.2.1 Norms -- 45.2.2 Induced Matrix Norm -- 45.3 Exercises -- 46 Functions of Several Variables -- 46.1 The Functions and Their Representations -- 46.2 Some Topological Terms -- 46.3 Consequences, Limits, Continuity -- 46.4 Exercises -- 47 Partial Differentiation: Gradient, Hessian Matrix, Jacobian Matrix -- 47.1 The Gradient -- 47.2 The Hessian Matrix -- 47.3 The Jacobian Matrix -- 47.4 Exercises -- 48 Applications of Partial Derivatives -- 48.1 The (Multidimensional) Newton Method -- 48.2 Taylor Development -- 48.2.1 The Zeroth, First and Second Taylor Polynomial -- 48.2.2 The General Taylor polynomial -- 48.3 Exercises -- 49 Extreme Value Determination -- 49.1 Local and Global Extrema -- 49.2 Determination of Extrema and Extremal Points -- 49.3 Exercises -- 50 Extreme Value Determination Under Constraints -- 50.1 Extrema Under Constraints -- 50.2 The Substitution Method -- 50.3 The Method of Lagrange Multipliers.
50.4 Extrema Under Multiple Constraints.
Record Nr. UNINA-9910629289203321
Karpfinger Christian  
Berlin, Germany : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Autore Karpfinger Christian
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2022]
Descrizione fisica 1 online resource (1015 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Calculus
Differential equations
Àlgebra lineal
Càlcul
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783662654583
9783662654576
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Speech, Symbols and Sets -- 1.1 Speech Patterns and Symbols in Mathematics -- 1.1.1 Junctors -- 1.1.2 Quantifiers -- 1.2 Summation and Product Symbol -- 1.3 Powers and Roots -- 1.4 Symbols of Set Theory -- 1.5 Exercises -- 2 The Natural Numbers, Integers and Rational Numbers -- 2.1 The Natural Numbers -- 2.2 The Integers -- 2.3 The Rational Numbers -- 2.4 Exercises -- 3 The Real Numbers -- 3.1 Basics -- 3.2 Real Intervals -- 3.3 The Absolute Value of a Real Number -- 3.4 n-th Roots -- 3.5 Solving Equations and Inequalities -- 3.6 Maximum, Minimum, Supremum and Infimum -- 3.7 Exercises -- 4 Machine Numbers -- 4.1 b-adic Representation of Real Numbers -- 4.2 Floating Point Numbers -- 4.2.1 Machine Numbers -- 4.2.2 Machine Epsilon, Rounding and Floating Point Arithmetic -- 4.2.3 Loss of Significance -- 4.3 Exercises -- 5 Polynomials -- 5.1 Polynomials: Multiplication and Division -- 5.2 Factorization of Polynomials -- 5.3 Evaluating Polynomials -- 5.4 Partial Fraction Decomposition -- 5.5 Exercises -- 6 Trigonometric Functions -- 6.1 Sine and Cosine -- 6.2 Tangent and Cotangent -- 6.3 The Inverse Functions of the Trigonometric Functions -- 6.4 Exercises -- 7 Complex Numbers: Cartesian Coordinates -- 7.1 Construction of C -- 7.2 The Imaginary Unit and Other Terms -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Exercises -- 8 Complex Numbers: Polar Coordinates -- 8.1 The Polar Representation -- 8.2 Applications of the Polar Representation -- 8.3 Exercises -- 9 Linear Systems of Equations -- 9.1 The Gaussian Elimination Method -- 9.2 The Rank of a Matrix -- 9.3 Homogeneous Linear Systems of Equations -- 9.4 Exercises -- 10 Calculating with Matrices -- 10.1 Definition of Matrices and Some Special Matrices.
10.2 Arithmetic Operations -- 10.3 Inverting Matrices -- 10.4 Calculation Rules -- 10.5 Exercises -- 11 LR-Decomposition of a Matrix -- 11.1 Motivation -- 11.2 The LR-Decomposition: Simplified Variant -- 11.3 The LR-Decomposition: General Variant -- 11.4 The LR-Decomposition-with Column Pivot Search -- 11.5 Exercises -- 12 The Determinant -- 12.1 Definition of the Determinant -- 12.2 Calculation of the Determinant -- 12.3 Applications of the Determinant -- 12.4 Exercises -- 13 Vector Spaces -- 13.1 Definition and Important Examples -- 13.2 Subspaces -- 13.3 Exercises -- 14 Generating Systems and Linear (In)Dependence -- 14.1 Linear Combinations -- 14.2 The Span of X -- 14.3 Linear (In)Dependence -- 14.4 Exercises -- 15 Bases of Vector Spaces -- 15.1 Bases -- 15.2 Applications to Matrices and Systems of Linear Equations -- 15.3 Exercises -- 16 Orthogonality I -- 16.1 Scalar Products -- 16.2 Length, Distance, Angle and Orthogonality -- 16.3 Orthonormal Bases -- 16.4 Orthogonal Decomposition and Linear Combination with Respect to an ONB -- 16.5 Orthogonal Matrices -- 16.6 Exercises -- 17 Orthogonality II -- 17.1 The Orthonormalization Method of Gram and Schmidt -- 17.2 The Vector Product and the (Scalar) Triple Product -- 17.3 The Orthogonal Projection -- 17.4 Exercises -- 18 The Linear Equalization Problem -- 18.1 The Linear Equalization Problem and Its Solution -- 18.2 The Orthogonal Projection -- 18.3 Solution of an Over-Determined Linear System of Equations -- 18.4 The Method of Least Squares -- 18.5 Exercises -- 19 The QR-Decomposition of a Matrix -- 19.1 Full and Reduced QR-Decomposition -- 19.2 Construction of the QR-Decomposition -- 19.3 Applications of the QR-Decomposition -- 19.3.1 Solving a System of Linear Equations -- 19.3.2 Solving the Linear Equalization Problem -- 19.4 Exercises -- 20 Sequences -- 20.1 Terms.
20.2 Convergence and Divergence of Sequences -- 20.3 Exercises -- 21 Calculation of Limits of Sequences -- 21.1 Determining Limits of Explicit Sequences -- 21.2 Determining Limits of Recursive Sequences -- 21.3 Exercises -- 22 Series -- 22.1 Definition and Examples -- 22.2 Convergence Criteria -- 22.3 Exercises -- 23 Mappings -- 23.1 Terms and Examples -- 23.2 Composition, Injective, Surjective, Bijective -- 23.3 The Inverse Mapping -- 23.4 Bounded and Monotone Functions -- 23.5 Exercises -- 24 Power Series -- 24.1 The Domain of Convergence of Real Power Series -- 24.2 The Domain of Convergence of Complex Power Series -- 24.3 The Exponential and the Logarithmic Function -- 24.4 The Hyperbolic Functions -- 24.5 Exercises -- 25 Limits and Continuity -- 25.1 Limits of Functions -- 25.2 Asymptotes of Functions -- 25.3 Continuity -- 25.4 Important Theorems about Continuous Functions -- 25.5 The Bisection Method -- 25.6 Exercises -- 26 Differentiation -- 26.1 The Derivative and the Derivative Function -- 26.2 Derivation Rules -- 26.3 Numerical Differentiation -- 26.4 Exercises -- 27 Applications of Differential Calculus I -- 27.1 Monotonicity -- 27.2 Local and Global Extrema -- 27.3 Determination of Extrema and Extremal Points -- 27.4 Convexity -- 27.5 The Rule of L'Hospital -- 27.6 Exercises -- 28 Applications of Differential Calculus II -- 28.1 The Newton Method -- 28.2 Taylor Expansion -- 28.3 Remainder Estimates -- 28.4 Determination of Taylor Series -- 28.5 Exercises -- 29 Polynomial and Spline Interpolation -- 29.1 Polynomial Interpolation -- 29.2 Construction of Cubic Splines -- 29.3 Exercises -- 30 Integration I -- 30.1 The Definite Integral -- 30.2 The Indefinite Integral -- 30.3 Exercises -- 31 Integration II -- 31.1 Integration of Rational Functions -- 31.2 Rational Functions in Sine and Cosine -- 31.3 Numerical Integration.
31.4 Volumes and Surfaces of Solids of Revolution -- 31.5 Exercises -- 32 Improper Integrals -- 32.1 Calculation of Improper Integrals -- 32.2 The Comparison Test for Improper Integrals -- 32.3 Exercises -- 33 Separable and Linear Differential Equations of First Order -- 33.1 First Differential Equations -- 33.2 Separable Differential Equations -- 33.2.1 The Procedure for Solving a Separable Differential Equation -- 33.2.2 Initial Value Problems -- 33.3 The Linear Differential Equation of First Order -- 33.4 Exercises -- 34 Linear Differential Equations with Constant Coefficients -- 34.1 Homogeneous Linear Differential Equations with Constant Coefficients -- 34.2 Inhomogeneous Linear Differential Equations with Constant Coefficients -- 34.2.1 Variation of Parameters -- 34.2.2 Approach of the Right-Hand Side Type -- 34.3 Exercises -- 35 Some Special Types of Differential Equations -- 35.1 The Homogeneous Differential Equation -- 35.2 The Euler Differential Equation -- 35.3 Bernoulli's Differential Equation -- 35.4 The Riccati Differential Equation -- 35.5 The Power Series Approach -- 35.6 Exercises -- 36 Numerics of Ordinary Differential Equations I -- 36.1 First Procedure -- 36.2 Runge-Kutta Method -- 36.3 Multistep Methods -- 36.4 Exercises -- 37 Linear Mappings and Transformation Matrices -- 37.1 Definitions and Examples -- 37.2 Image, Kernel and the Dimensional Formula -- 37.3 Coordinate Vectors -- 37.4 Transformation Matrices -- 37.5 Exercises -- 38 Base Transformation -- 38.1 The Tansformation Matrix of the Composition of Linear Mappings -- 38.2 Base Transformation -- 38.3 The Two Methods for Determining Transformation Matrices -- 38.4 Exercises -- 39 Diagonalization: Eigenvalues and Eigenvectors -- 39.1 Eigenvalues and Eigenvectors of Matrices -- 39.2 Diagonalizing Matrices -- 39.3 The Characteristic Polynomial of a Matrix.
39.4 Diagonalization of Real Symmetric Matrices -- 39.5 Exercises -- 40 Numerical Calculation of Eigenvalues and Eigenvectors -- 40.1 Gerschgorin Circles -- 40.2 Vector Iteration -- 40.3 The Jacobian Method -- 40.4 The QR-Method -- 40.5 Exercises -- 41 Quadrics -- 41.1 Terms and First Examples -- 41.2 Transformation to Normal Form -- 41.3 Exercises -- 42 Schur Decomposition and Singular Value Decomposition -- 42.1 The Schur Decomposition -- 42.2 Calculation of the Schur Decomposition -- 42.3 Singular Value Decomposition -- 42.4 Determination of the Singular Value Decomposition -- 42.5 Exercises -- 43 The Jordan Normal Form I -- 43.1 Existence of the Jordan Normal Form -- 43.2 Generalized Eigenspaces -- 43.3 Exercises -- 44 The Jordan Normal Form II -- 44.1 Construction of a Jordan Base -- 44.2 Number and Size of Jordan Boxes -- 44.3 Exercises -- 45 Definiteness and Matrix Norms -- 45.1 Definiteness of Matrices -- 45.2 Matrix Norms -- 45.2.1 Norms -- 45.2.2 Induced Matrix Norm -- 45.3 Exercises -- 46 Functions of Several Variables -- 46.1 The Functions and Their Representations -- 46.2 Some Topological Terms -- 46.3 Consequences, Limits, Continuity -- 46.4 Exercises -- 47 Partial Differentiation: Gradient, Hessian Matrix, Jacobian Matrix -- 47.1 The Gradient -- 47.2 The Hessian Matrix -- 47.3 The Jacobian Matrix -- 47.4 Exercises -- 48 Applications of Partial Derivatives -- 48.1 The (Multidimensional) Newton Method -- 48.2 Taylor Development -- 48.2.1 The Zeroth, First and Second Taylor Polynomial -- 48.2.2 The General Taylor polynomial -- 48.3 Exercises -- 49 Extreme Value Determination -- 49.1 Local and Global Extrema -- 49.2 Determination of Extrema and Extremal Points -- 49.3 Exercises -- 50 Extreme Value Determination Under Constraints -- 50.1 Extrema Under Constraints -- 50.2 The Substitution Method -- 50.3 The Method of Lagrange Multipliers.
50.4 Extrema Under Multiple Constraints.
Record Nr. UNISA-996499871503316
Karpfinger Christian  
Berlin, Germany : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Change and variations : a history of differential equations to 1900 / / Jeremy Gray
Change and variations : a history of differential equations to 1900 / / Jeremy Gray
Autore Gray Jeremy <1947->
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XXII, 419 p. 44 illus., 13 illus. in color.)
Disciplina 515.35
Collana Springer undergraduate mathematics series
Soggetto topico Differential equations
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70575-7
9783030705749
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 The First Ordinary Differential Equations -- 2 Variational Problems and the Calculus -- 3 The Partial Differential Calculus -- 4 Rational Mechanics -- 5 Partial Differential Equations -- 6 Lagrange's General Theory -- 7 The Calculus of Variations -- 8 Monge and Solutions to Partial Differential Equations -- 9 Revision -- 10 The Heat Equation -- 11 Gauss and the Hypergeometric Equation -- 12 Existence Theorem -- 13 Riemann and Complex Function Theory -- 14 Riemann and the Hypergeometric Equation -- 15 Schwarz and the Complex Hypergeometric Equation -- 16 Complex Ordinary Differential Equations: Poincaré -- 17 More General Partial Differential Equations -- 18 Green's Functions and Dirichlet's Principle -- 19 Attempts on Laplace's Equation -- 20 Applied Wave Equations -- 21 Revision -- 22 Riemann's Shock Wave Paper -- 23 The Example of Minimal Surfaces -- 24 Partial Differential Equations and Mechanics -- 25 Geometrical Interpretations of Mechanics -- 26 The Calculus of Variations in the 19th Century -- 27 Poincaré and Mathematical Physics -- 28 Elliptic Equations and Regular Variational Problems -- 29 Hyperbolic Equations -- 30 Revision -- 32 Translations -- A Newton's Principia Mathematica -- B Characteristics -- C First-order Non-linear Equations -- D Green's Theorem and Heat Conduction -- E Complex Analysis -- F Möbius Transformations -- G Lipschitz and Picard -- H The Assessment -- Bibliography -- Index.
Record Nr. UNISA-996466408103316
Gray Jeremy <1947->  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Change and variations : a history of differential equations to 1900 / / Jeremy Gray
Change and variations : a history of differential equations to 1900 / / Jeremy Gray
Autore Gray Jeremy <1947->
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XXII, 419 p. 44 illus., 13 illus. in color.)
Disciplina 515.35
Collana Springer undergraduate mathematics series
Soggetto topico Differential equations
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70575-7
9783030705749
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 The First Ordinary Differential Equations -- 2 Variational Problems and the Calculus -- 3 The Partial Differential Calculus -- 4 Rational Mechanics -- 5 Partial Differential Equations -- 6 Lagrange's General Theory -- 7 The Calculus of Variations -- 8 Monge and Solutions to Partial Differential Equations -- 9 Revision -- 10 The Heat Equation -- 11 Gauss and the Hypergeometric Equation -- 12 Existence Theorem -- 13 Riemann and Complex Function Theory -- 14 Riemann and the Hypergeometric Equation -- 15 Schwarz and the Complex Hypergeometric Equation -- 16 Complex Ordinary Differential Equations: Poincaré -- 17 More General Partial Differential Equations -- 18 Green's Functions and Dirichlet's Principle -- 19 Attempts on Laplace's Equation -- 20 Applied Wave Equations -- 21 Revision -- 22 Riemann's Shock Wave Paper -- 23 The Example of Minimal Surfaces -- 24 Partial Differential Equations and Mechanics -- 25 Geometrical Interpretations of Mechanics -- 26 The Calculus of Variations in the 19th Century -- 27 Poincaré and Mathematical Physics -- 28 Elliptic Equations and Regular Variational Problems -- 29 Hyperbolic Equations -- 30 Revision -- 32 Translations -- A Newton's Principia Mathematica -- B Characteristics -- C First-order Non-linear Equations -- D Green's Theorem and Heat Conduction -- E Complex Analysis -- F Möbius Transformations -- G Lipschitz and Picard -- H The Assessment -- Bibliography -- Index.
Record Nr. UNINA-9910484121003321
Gray Jeremy <1947->  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2023]
Descrizione fisica 1 online resource (396 pages)
Disciplina 531
Soggetto topico Continuum mechanics
Differential equations
Mecànica dels medis continus
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031192524
9783031192517
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface -- References -- Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Typical Ocean Densities -- 3.1. Linear Density -- 3.2. Equation of State by TEOS-10 -- 3.3. Equation of State by McDongall-Jacket-Wright-Feistel -- 3.4. Equation of State by UNESCO-80 -- 4. Main Result -- 5. Estimates for the Local Existence -- 6. A Priori Estimates -- 7. Proof of Theorem 4.1 -- 7.1. Local Wellposedness -- 7.2. Global Wellposedness -- Appendix A. Semilinear Evolution Equations and Maximal Lr-Regularity -- References -- On the Global Existence for the Compressible Euler-Riesz System -- Abstract -- Introduction -- 1. Main Results -- 2. A Local in Time Result for Non-decaying Data -- 2.1. A Priori Estimates -- 2.2. About the Proof of Existence -- 2.3. Uniqueness -- 3. A Global Existence Result -- 3.1. A Priori Estimates -- 3.2. Existence -- 3.3. The Proof of Uniqueness -- 3.4. Instability of Nontrivial Static Solutions in the Attractive Case -- 4. About Ideal Gases -- 4.1. Local Existence -- 4.2. Global Existence -- 4.3. Remark on Static Solutions -- Appendix -- Acknowledgements -- References -- Rotation Problem for a Two-Phase Drop -- Abstract -- 1. Introduction -- 2. Linear Problem -- 3. The Nonlinear Problem -- References -- On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle -- Abstract -- 1. Introduction -- 2. Notation -- 3. Main Results -- 4. The Resolvent Problem in the Whole Space -- 5. The Resolvent Problem in an Exterior Domain -- 6. The Time-Periodic Problem -- References -- Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit -- Abstract -- 1. Introduction -- 2. Preliminary Material -- 2.1. Mathematical Theory of the Closed System.
2.2. Transport Coefficients -- 2.3. Equation of State -- 2.4. Relative Energy -- 3. Main Results -- 3.1. Unconditional Convergence in the Absence of Boundary Layer -- 3.2. Conditional Result: Viscous Boundary Layer -- 4. Consistency of the Vanishing Dissipation/Radiation Approximation -- 4.1. Temperature for the Euler System -- 4.2. Consistency -- 4.2.1. Viscous Stress Consistency -- 4.2.2. Heat Flux Consistency -- 4.2.3. Radiation Entropy Convective Flux Consistency -- 5. Convergence -- 5.1. Velocity Regularization -- 5.2. Application of the Relative Energy Inequality -- 5.3. Integrals Controlled by the Consistency Estimates -- 5.4. Integrals Independent of the Boundary Layer -- 5.5. Boundary Layer -- 5.5.1. Viscous Stress -- 5.5.2. Convective Term -- 5.6. Strong Convergence -- References -- On the Hydrostatic Approximation of Compressible Anisotropic Navier-Stokes Equations-Rigorous Justification -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 3.1. Dissipative Weak Solutions of CNS -- 3.2. Strong Solution of CPE -- 3.3. Versatile Relative Entropy Inequality -- 3.4. Main Result -- 4. Convergence -- 4.1. Main Idea of Proof -- 4.2. Step 1 -- 4.3. Step 2 -- 4.4. Step 3 -- Acknowledgements -- References -- A Route to Chaos in Rayleigh-Bénard Heat Convection -- Abstract -- 1. Introduction -- 2. linear Stability and Critical Rayleigh Number -- 3. Routes to Chaos -- 3.1. Roll Solutions on Bifurcation Branches in the Large -- 3.2. Time Evolution of Roll Solutions and the Secondary Hopf Bifurcation -- 3.3. Concluding Remark -- Acknowledgements -- References -- Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method -- Abstract -- 1. Introduction -- 2. Notations and Main Results -- 3. Preliminaries -- 4. Proof of Main Results -- Acknowledgements -- References.
Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application -- Abstract -- 1. Introduction -- 2. Notation and Main Results -- 2.1. Notation -- 2.2. Main Results -- 3. Preliminaries -- 3.1. Some Inequalities -- 3.2. Compact Embeddings -- 3.3. Results of the Large Resolvent Parameter -- 3.4. Maximal Regularity -- 4. The Problem in Bounded Domains -- 4.1. Existence of Solutions -- 4.2. Uniqueness of Solutions -- 4.3. A Priori Estimates -- 4.4. Proof of Theorem 2.5 -- 4.5. Proof of Theorem 2.6 -- 5. The Whole Space Problem -- 5.1. Representation Formulas of Solutions -- 5.2. Estimates of P(ξ,λ) for γ=0. -- 5.3. Estimates of P(ξ,λ) for γ> -- 0. -- 5.4. Proof of Theorem 5.1 -- 6. The Problem in Exterior Domains -- 6.1. Construction of Parametrix -- 6.2. Uniqueness of Solutions -- 6.3. A Priori Estimates -- 6.4. An Auxiliary Problem -- 6.5. Proof of Theorem 2.1 -- 7. Application to a Nonlinear Problem -- 7.1. Generation of an Analytic C0-Semigroup -- 7.2. Maximal Regularity with Exponential Stability -- 7.3. Estimates of Nonlinear Terms -- 7.4. Global Solvability of the Nonlinear Problem -- References -- Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Analysis of the Linearized Operator -- 3.1. Settings and Basic Results -- 3.2. Verification of Assumption 4.6 -- 3.3. Estimates for the Semigroup -- 4. Abstract Results -- 5. Appendix: Basic Formulas of Differential Geometry -- Acknowledgements -- References -- Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces -- Abstract -- 1. Introduction -- 2. Functional Spaces and the Main Result -- 3. Auxiliary Results and Linear Theory -- 4. A Priori Estimates -- 4.1. Velocity Bounds -- 4.2. Estimates for the Density -- 5. Existence -- Acknowledgements -- References.
Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals -- Abstract -- 1. Introduction -- 2. Maximal Lp-Lq Regularity -- 2.1. mathcalR-boundedness of Solution Operators -- 2.2. A Proof of Theorem 2.1 -- 3. Decay Property of Solutions to the Linearized Problem -- 3.1. Decay Estimates for d -- 3.2. Decay Estimates for U and mathbbQ -- 3.2.1. Analysis of Low Frequency Parts -- 3.2.2. Analysis of High Frequency Parts -- 4. A Proof of Theorem 1.1 -- 4.1. Analysis of Time Shifted Equations -- 4.2. Analysis of Compensation Equations -- 4.2.1. Estimates of Spatial Derivatives in Lp-Lq -- 4.2.2. Estimates of Time Derivatives in Lp-Lq -- 4.2.3. Estimates of the Lower Order Term in Linfty-Lq -- 4.3. Conclusion -- References -- Maximal Regularity for Compressible Two-Fluid System -- Abstract -- 1. Introduction -- 1.1. Notation -- 1.2. Main Results -- 1.3. Discussion -- 2. Lagrangian Coordinates -- 3. Local Well-Posedness -- 3.1. Linearization Around the Initial Condition -- 3.2. Maximal Regularity -- 3.3. Preliminary Estimates -- 3.4. Estimate of the Right Hand Side of (3.3) -- 3.5. Contraction Argument-Proof of Theorem 1.1 -- 4. Global Well-Posedness -- 4.1. Linearization Around the Constant State -- 4.2. Exponential Decay -- 4.3. Bounds for Nonlinearities -- 4.4. Proof of Theorem 1.2 -- Appendix -- Acknowledgements -- References -- Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature -- Abstract -- 1. Introduction -- 2. Formulation of the Problem: Main Result -- 3. Weak Compactness of Weak and Variational Entropy Ballistic Solutions -- 3.1. A Priori Estimates -- 3.2. Weak Compactness -- 4. Construction of the Solution -- References -- A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations -- Abstract -- 1. Introduction -- 2. Auxiliary Facts.
3. Proof of Proposition 1.4 -- 4. Proof of Theorem 1.3 -- Acknowledgements -- References -- Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle -- Abstract -- 1. Introduction -- 2. Results -- 2.1. Notation -- 2.2. Evolution Operator -- 2.3. Main Results -- 3. Proof of Theorem 2.1 -- 3.1. Weak Form of the Integral Equation -- 3.2. Regularity in x -- 3.3. Regularity in t and the Pressure -- 4. Proof of Theorem 2.2 -- 4.1. Reduction to the Whole Space Problem -- 4.2. Integral Equation for the Whole Space Problem -- 4.3. Reconstruction Procedure -- References.
Record Nr. UNINA-9910633925403321
Cham, Switzerland : , : Birkhäuser, , [2023]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Collected papers in honor Yoshihiro Shibata / / Tohru Ozawa, editor
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2023]
Descrizione fisica 1 online resource (396 pages)
Disciplina 531
Soggetto topico Continuum mechanics
Differential equations
Mecànica dels medis continus
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031192524
9783031192517
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface -- References -- Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Typical Ocean Densities -- 3.1. Linear Density -- 3.2. Equation of State by TEOS-10 -- 3.3. Equation of State by McDongall-Jacket-Wright-Feistel -- 3.4. Equation of State by UNESCO-80 -- 4. Main Result -- 5. Estimates for the Local Existence -- 6. A Priori Estimates -- 7. Proof of Theorem 4.1 -- 7.1. Local Wellposedness -- 7.2. Global Wellposedness -- Appendix A. Semilinear Evolution Equations and Maximal Lr-Regularity -- References -- On the Global Existence for the Compressible Euler-Riesz System -- Abstract -- Introduction -- 1. Main Results -- 2. A Local in Time Result for Non-decaying Data -- 2.1. A Priori Estimates -- 2.2. About the Proof of Existence -- 2.3. Uniqueness -- 3. A Global Existence Result -- 3.1. A Priori Estimates -- 3.2. Existence -- 3.3. The Proof of Uniqueness -- 3.4. Instability of Nontrivial Static Solutions in the Attractive Case -- 4. About Ideal Gases -- 4.1. Local Existence -- 4.2. Global Existence -- 4.3. Remark on Static Solutions -- Appendix -- Acknowledgements -- References -- Rotation Problem for a Two-Phase Drop -- Abstract -- 1. Introduction -- 2. Linear Problem -- 3. The Nonlinear Problem -- References -- On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle -- Abstract -- 1. Introduction -- 2. Notation -- 3. Main Results -- 4. The Resolvent Problem in the Whole Space -- 5. The Resolvent Problem in an Exterior Domain -- 6. The Time-Periodic Problem -- References -- Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit -- Abstract -- 1. Introduction -- 2. Preliminary Material -- 2.1. Mathematical Theory of the Closed System.
2.2. Transport Coefficients -- 2.3. Equation of State -- 2.4. Relative Energy -- 3. Main Results -- 3.1. Unconditional Convergence in the Absence of Boundary Layer -- 3.2. Conditional Result: Viscous Boundary Layer -- 4. Consistency of the Vanishing Dissipation/Radiation Approximation -- 4.1. Temperature for the Euler System -- 4.2. Consistency -- 4.2.1. Viscous Stress Consistency -- 4.2.2. Heat Flux Consistency -- 4.2.3. Radiation Entropy Convective Flux Consistency -- 5. Convergence -- 5.1. Velocity Regularization -- 5.2. Application of the Relative Energy Inequality -- 5.3. Integrals Controlled by the Consistency Estimates -- 5.4. Integrals Independent of the Boundary Layer -- 5.5. Boundary Layer -- 5.5.1. Viscous Stress -- 5.5.2. Convective Term -- 5.6. Strong Convergence -- References -- On the Hydrostatic Approximation of Compressible Anisotropic Navier-Stokes Equations-Rigorous Justification -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 3.1. Dissipative Weak Solutions of CNS -- 3.2. Strong Solution of CPE -- 3.3. Versatile Relative Entropy Inequality -- 3.4. Main Result -- 4. Convergence -- 4.1. Main Idea of Proof -- 4.2. Step 1 -- 4.3. Step 2 -- 4.4. Step 3 -- Acknowledgements -- References -- A Route to Chaos in Rayleigh-Bénard Heat Convection -- Abstract -- 1. Introduction -- 2. linear Stability and Critical Rayleigh Number -- 3. Routes to Chaos -- 3.1. Roll Solutions on Bifurcation Branches in the Large -- 3.2. Time Evolution of Roll Solutions and the Secondary Hopf Bifurcation -- 3.3. Concluding Remark -- Acknowledgements -- References -- Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method -- Abstract -- 1. Introduction -- 2. Notations and Main Results -- 3. Preliminaries -- 4. Proof of Main Results -- Acknowledgements -- References.
Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application -- Abstract -- 1. Introduction -- 2. Notation and Main Results -- 2.1. Notation -- 2.2. Main Results -- 3. Preliminaries -- 3.1. Some Inequalities -- 3.2. Compact Embeddings -- 3.3. Results of the Large Resolvent Parameter -- 3.4. Maximal Regularity -- 4. The Problem in Bounded Domains -- 4.1. Existence of Solutions -- 4.2. Uniqueness of Solutions -- 4.3. A Priori Estimates -- 4.4. Proof of Theorem 2.5 -- 4.5. Proof of Theorem 2.6 -- 5. The Whole Space Problem -- 5.1. Representation Formulas of Solutions -- 5.2. Estimates of P(ξ,λ) for γ=0. -- 5.3. Estimates of P(ξ,λ) for γ> -- 0. -- 5.4. Proof of Theorem 5.1 -- 6. The Problem in Exterior Domains -- 6.1. Construction of Parametrix -- 6.2. Uniqueness of Solutions -- 6.3. A Priori Estimates -- 6.4. An Auxiliary Problem -- 6.5. Proof of Theorem 2.1 -- 7. Application to a Nonlinear Problem -- 7.1. Generation of an Analytic C0-Semigroup -- 7.2. Maximal Regularity with Exponential Stability -- 7.3. Estimates of Nonlinear Terms -- 7.4. Global Solvability of the Nonlinear Problem -- References -- Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Analysis of the Linearized Operator -- 3.1. Settings and Basic Results -- 3.2. Verification of Assumption 4.6 -- 3.3. Estimates for the Semigroup -- 4. Abstract Results -- 5. Appendix: Basic Formulas of Differential Geometry -- Acknowledgements -- References -- Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces -- Abstract -- 1. Introduction -- 2. Functional Spaces and the Main Result -- 3. Auxiliary Results and Linear Theory -- 4. A Priori Estimates -- 4.1. Velocity Bounds -- 4.2. Estimates for the Density -- 5. Existence -- Acknowledgements -- References.
Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals -- Abstract -- 1. Introduction -- 2. Maximal Lp-Lq Regularity -- 2.1. mathcalR-boundedness of Solution Operators -- 2.2. A Proof of Theorem 2.1 -- 3. Decay Property of Solutions to the Linearized Problem -- 3.1. Decay Estimates for d -- 3.2. Decay Estimates for U and mathbbQ -- 3.2.1. Analysis of Low Frequency Parts -- 3.2.2. Analysis of High Frequency Parts -- 4. A Proof of Theorem 1.1 -- 4.1. Analysis of Time Shifted Equations -- 4.2. Analysis of Compensation Equations -- 4.2.1. Estimates of Spatial Derivatives in Lp-Lq -- 4.2.2. Estimates of Time Derivatives in Lp-Lq -- 4.2.3. Estimates of the Lower Order Term in Linfty-Lq -- 4.3. Conclusion -- References -- Maximal Regularity for Compressible Two-Fluid System -- Abstract -- 1. Introduction -- 1.1. Notation -- 1.2. Main Results -- 1.3. Discussion -- 2. Lagrangian Coordinates -- 3. Local Well-Posedness -- 3.1. Linearization Around the Initial Condition -- 3.2. Maximal Regularity -- 3.3. Preliminary Estimates -- 3.4. Estimate of the Right Hand Side of (3.3) -- 3.5. Contraction Argument-Proof of Theorem 1.1 -- 4. Global Well-Posedness -- 4.1. Linearization Around the Constant State -- 4.2. Exponential Decay -- 4.3. Bounds for Nonlinearities -- 4.4. Proof of Theorem 1.2 -- Appendix -- Acknowledgements -- References -- Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature -- Abstract -- 1. Introduction -- 2. Formulation of the Problem: Main Result -- 3. Weak Compactness of Weak and Variational Entropy Ballistic Solutions -- 3.1. A Priori Estimates -- 3.2. Weak Compactness -- 4. Construction of the Solution -- References -- A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations -- Abstract -- 1. Introduction -- 2. Auxiliary Facts.
3. Proof of Proposition 1.4 -- 4. Proof of Theorem 1.3 -- Acknowledgements -- References -- Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle -- Abstract -- 1. Introduction -- 2. Results -- 2.1. Notation -- 2.2. Evolution Operator -- 2.3. Main Results -- 3. Proof of Theorem 2.1 -- 3.1. Weak Form of the Integral Equation -- 3.2. Regularity in x -- 3.3. Regularity in t and the Pressure -- 4. Proof of Theorem 2.2 -- 4.1. Reduction to the Whole Space Problem -- 4.2. Integral Equation for the Whole Space Problem -- 4.3. Reconstruction Procedure -- References.
Record Nr. UNISA-996499865603316
Cham, Switzerland : , : Birkhäuser, , [2023]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui