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Controllability and Stabilization of Parabolic Equations / / by Viorel Barbu
| Controllability and Stabilization of Parabolic Equations / / by Viorel Barbu |
| Autore | Barbu Viorel |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2018 |
| Descrizione fisica | 1 online resource (x, 226 pages) |
| Disciplina | 629.8312 |
| Collana | PNLDE Subseries in Control |
| Soggetto topico |
System theory
Partial differential equations Control engineering Engineering mathematics Systems Theory, Control Partial Differential Equations Control and Systems Theory Engineering Mathematics |
| ISBN | 3-319-76666-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Acronyms -- Preliminaries -- The Carleman Inequality for Linear Parabolic Equations -- Exact Controllability of Parabolic Equations -- Internal Controllability of Parabolic Equations with Inputs in Coefficients -- Feedback Stabilization of Semilinear Parabolic Equations -- Boundary Stabilization of Navier–Stokes Equations -- Index. |
| Record Nr. | UNINA-9910300112603321 |
Barbu Viorel
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Differential Equations / / by Viorel Barbu
| Differential Equations / / by Viorel Barbu |
| Autore | Barbu Viorel |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XI, 224 p. 16 illus.) |
| Disciplina | 515.353 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Differential equations
System theory Partial differential equations Ordinary Differential Equations Systems Theory, Control Partial Differential Equations |
| ISBN | 3-319-45261-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Existence and uniqueness for the Cauchy problem -- Systems of linear differential equations -- Stability theory -- Prime integrals and first-order partial differential equations. |
| Record Nr. | UNINA-9910254071303321 |
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Barbu Viorel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts
| Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts |
| Autore | Barbu Viorel |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer, , 2024 |
| Descrizione fisica | 1 online resource (219 pages) |
| Altri autori (Persone) | RöcknerMichael |
| Collana | Lecture Notes in Mathematics Series |
| ISBN |
9783031617348
9783031617331 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- Symbols and Notation -- 1 Introduction -- 2 Existence of Nonlinear Fokker-Planck Flows -- 2.1 Existence for the NFPE (2.1) -- 2.2 Existence and Uniqueness of Mild Solutions to Isotropic NFPE -- 2.3 Uniqueness of Distributional Solutions to NFPE -- 2.4 NFPEs with Superlinear Diffusion -- 2.5 Smoothing Effect of NFP Flow on Initial Data -- 2.6 NFPE with a Measure as Initial Datum -- 2.7 NFPEs with Discontinuous Coefficients -- 2.8 NFPE with Fractional Laplacian -- 2.9 A Splitting Formula for NFPE -- Comments to Chap. 2 -- 3 Time Dependent Fokker-Planck Equations -- 3.1 Time Varying Fokker-Planck Flows -- 3.2 Fokker-Planck Periodic Flows -- Comments to Chap. 3 -- 4 Convergence to Equilibrium of Nonlinear Fokker-Planck Flows -- 4.1 The H-Theorem for the Nonlinear Fokker-Planck Equations -- 4.2 Attractors for Nonlinear Fokker-Planck Flows -- 4.3 The Ergodicity of Nonlinear Fokker-Planck Flows -- Comments to Chap. 4 -- 5 Markov Processes Associated with Nonlinear Fokker-Planck Equations -- 5.1 Fokker-Planck Equations and McKean-Vlasov SDEs -- 5.2 Uniqueness of Weak Solutions to McKean-Vlasov SDEs and Corresponding Nonlinear Markov Processes -- 5.3 Strong Solutions to McKean-Vlasov SDEs -- 6 Appendix -- 6.1 Nonlinear m-Accretive Operators -- 6.2 Semigroups of Contractions in Banach Spaces -- 6.3 Riesz Potentials -- References -- Index. |
| Record Nr. | UNINA-9910865237703321 |
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Barbu Viorel
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| Cham : , : Springer, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Stochastic Porous Media Equations [[electronic resource] /] / by Viorel Barbu, Giuseppe Da Prato, Michael Röckner
| Stochastic Porous Media Equations [[electronic resource] /] / by Viorel Barbu, Giuseppe Da Prato, Michael Röckner |
| Autore | Barbu Viorel |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (IX, 202 p.) |
| Disciplina | 519.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Probabilities
Partial differential equations Fluids Probability Theory and Stochastic Processes Partial Differential Equations Fluid- and Aerodynamics |
| ISBN | 3-319-41069-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword -- Preface -- Introduction -- Equations with Lipschitz nonlinearities -- Equations with maximal monotone nonlinearities -- Variational approach to stochastic porous media equations -- L1-based approach to existence theory for stochastic porous media equations -- The stochastic porous media equations in Rd -- Transition semigroups and ergodicity of invariant measures -- Kolmogorov equations -- A Two analytical inequalities -- Bibliography -- Glossary -- Translator’s note -- Index. |
| Record Nr. | UNISA-996466477903316 |
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Barbu Viorel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Stochastic Porous Media Equations / / by Viorel Barbu, Giuseppe Da Prato, Michael Röckner
| Stochastic Porous Media Equations / / by Viorel Barbu, Giuseppe Da Prato, Michael Röckner |
| Autore | Barbu Viorel |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (IX, 202 p.) |
| Disciplina | 519.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Probabilities
Partial differential equations Fluids Probability Theory and Stochastic Processes Partial Differential Equations Fluid- and Aerodynamics |
| ISBN | 3-319-41069-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword -- Preface -- Introduction -- Equations with Lipschitz nonlinearities -- Equations with maximal monotone nonlinearities -- Variational approach to stochastic porous media equations -- L1-based approach to existence theory for stochastic porous media equations -- The stochastic porous media equations in Rd -- Transition semigroups and ergodicity of invariant measures -- Kolmogorov equations -- A Two analytical inequalities -- Bibliography -- Glossary -- Translator’s note -- Index. |
| Record Nr. | UNINA-9910136471503321 |
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Barbu Viorel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani
| Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani |
| Autore | Barbu Viorel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Navier-Stokes equations
Boundary layer Mathematical optimization Riccati equation |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0456-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""Chapter 2. Main results""; ""Chapter 3. Proof of Theorems 2.1 and 2.2 on the linearized system ( 2.4): d = 3""; ""3.1. Abstract models of the linearized problem ( 2.3). Regularity ""; ""3.2. The operator D*A, D*:Hâ??(L[sup(2)](T))[sub(D)]""; ""3.3. A critical boundary property related to the boundary c.c. in ( 3.1.2e) ""; ""3.4. Some technical preliminaries; space and system decomposition ""
""3.5. Theorem 2.1, general case d = 3: An infinite-dimensional open�loop boundary controller g satisfying the FCC (3.1.22)�(3.1.24) for the linearized system�""""3.6. Feedback stabilization of the unstable [sub(Z)]N�system ( 3.4.9) on Z[sup(u)][sub(N)] under the FDSA""; ""3.7. Theorem 2.2, case d = 3 under the FDSA: An open�loop boundary controller g satisfying the FCC ( 3.1.22)�( 3.1.24) for the linearized system�"" ""Chapter 4. Boundary feedback uniform stabilization of the linearized system( 3.1.4) via an optimal control problem and corresponding Riccati theory. Case d = 3""""4.0. Orientation""; ""4.1. The optimal control problem ( Case d = 3)""; ""4.2. Optimal feedback dynamics: the feedback semigroup and its generator on W""; ""4.3. Feedback synthesis via the Riccati operator""; ""4.4. Identification of the Riccati operator R in ( 4.1.8) with the operator R[sub(1)] in ( 4.3.1)"" ""4.5. A Riccati�type algebraic equation satisfied by the operator R on the domain D(A[sup2)][Sub(R)], Where A[sub(R)] is the feedback generator""""Chapter 5. Theorem 2.3(i): Well�posedness of the Navier�Stokes equations with Riccati�based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Navier�Stokes equations with Riccati�based boundary feedback control""; ""Chapter 7. A PDE�interpretation of the abstract results in Sections 5 and 6""; ""Appendix A. Technical Material Complementing Section 3.1"" ""B.3. Completion of the proof of Theorem 2.5 and Theorem 2.6 for the N�S model (1.1), d = 2"" |
| Record Nr. | UNINA-9910480400503321 |
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Barbu Viorel
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| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani
| Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani |
| Autore | Barbu Viorel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Navier-Stokes equations
Boundary layer Mathematical optimization Riccati equation |
| ISBN | 1-4704-0456-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""Chapter 2. Main results""; ""Chapter 3. Proof of Theorems 2.1 and 2.2 on the linearized system ( 2.4): d = 3""; ""3.1. Abstract models of the linearized problem ( 2.3). Regularity ""; ""3.2. The operator D*A, D*:Hâ??(L[sup(2)](T))[sub(D)]""; ""3.3. A critical boundary property related to the boundary c.c. in ( 3.1.2e) ""; ""3.4. Some technical preliminaries; space and system decomposition ""
""3.5. Theorem 2.1, general case d = 3: An infinite-dimensional open�loop boundary controller g satisfying the FCC (3.1.22)�(3.1.24) for the linearized system�""""3.6. Feedback stabilization of the unstable [sub(Z)]N�system ( 3.4.9) on Z[sup(u)][sub(N)] under the FDSA""; ""3.7. Theorem 2.2, case d = 3 under the FDSA: An open�loop boundary controller g satisfying the FCC ( 3.1.22)�( 3.1.24) for the linearized system�"" ""Chapter 4. Boundary feedback uniform stabilization of the linearized system( 3.1.4) via an optimal control problem and corresponding Riccati theory. Case d = 3""""4.0. Orientation""; ""4.1. The optimal control problem ( Case d = 3)""; ""4.2. Optimal feedback dynamics: the feedback semigroup and its generator on W""; ""4.3. Feedback synthesis via the Riccati operator""; ""4.4. Identification of the Riccati operator R in ( 4.1.8) with the operator R[sub(1)] in ( 4.3.1)"" ""4.5. A Riccati�type algebraic equation satisfied by the operator R on the domain D(A[sup2)][Sub(R)], Where A[sub(R)] is the feedback generator""""Chapter 5. Theorem 2.3(i): Well�posedness of the Navier�Stokes equations with Riccati�based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Navier�Stokes equations with Riccati�based boundary feedback control""; ""Chapter 7. A PDE�interpretation of the abstract results in Sections 5 and 6""; ""Appendix A. Technical Material Complementing Section 3.1"" ""B.3. Completion of the proof of Theorem 2.5 and Theorem 2.6 for the N�S model (1.1), d = 2"" |
| Record Nr. | UNINA-9910788741903321 |
|
Barbu Viorel
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani
| Tangential boundary stabilization of Navier-Stokes equations / / Viorel Barbu, Irena Lasiecka, Roberto Triggiani |
| Autore | Barbu Viorel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Navier-Stokes equations
Boundary layer Mathematical optimization Riccati equation |
| ISBN | 1-4704-0456-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""Chapter 2. Main results""; ""Chapter 3. Proof of Theorems 2.1 and 2.2 on the linearized system ( 2.4): d = 3""; ""3.1. Abstract models of the linearized problem ( 2.3). Regularity ""; ""3.2. The operator D*A, D*:Hâ??(L[sup(2)](T))[sub(D)]""; ""3.3. A critical boundary property related to the boundary c.c. in ( 3.1.2e) ""; ""3.4. Some technical preliminaries; space and system decomposition ""
""3.5. Theorem 2.1, general case d = 3: An infinite-dimensional open�loop boundary controller g satisfying the FCC (3.1.22)�(3.1.24) for the linearized system�""""3.6. Feedback stabilization of the unstable [sub(Z)]N�system ( 3.4.9) on Z[sup(u)][sub(N)] under the FDSA""; ""3.7. Theorem 2.2, case d = 3 under the FDSA: An open�loop boundary controller g satisfying the FCC ( 3.1.22)�( 3.1.24) for the linearized system�"" ""Chapter 4. Boundary feedback uniform stabilization of the linearized system( 3.1.4) via an optimal control problem and corresponding Riccati theory. Case d = 3""""4.0. Orientation""; ""4.1. The optimal control problem ( Case d = 3)""; ""4.2. Optimal feedback dynamics: the feedback semigroup and its generator on W""; ""4.3. Feedback synthesis via the Riccati operator""; ""4.4. Identification of the Riccati operator R in ( 4.1.8) with the operator R[sub(1)] in ( 4.3.1)"" ""4.5. A Riccati�type algebraic equation satisfied by the operator R on the domain D(A[sup2)][Sub(R)], Where A[sub(R)] is the feedback generator""""Chapter 5. Theorem 2.3(i): Well�posedness of the Navier�Stokes equations with Riccati�based boundary feedback control. Case d = 3 ""; ""Chapter 6. Theorem 2.3(ii): Local uniform stability of the Navier�Stokes equations with Riccati�based boundary feedback control""; ""Chapter 7. A PDE�interpretation of the abstract results in Sections 5 and 6""; ""Appendix A. Technical Material Complementing Section 3.1"" ""B.3. Completion of the proof of Theorem 2.5 and Theorem 2.6 for the N�S model (1.1), d = 2"" |
| Record Nr. | UNINA-9910829172703321 |
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Barbu Viorel
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| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||