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Approssimazione numerica di traveling waves ed applicazioni. Tesi di laurea / laureanda Melissa Tarantino ; relatore Ivonne Sgura
| Approssimazione numerica di traveling waves ed applicazioni. Tesi di laurea / laureanda Melissa Tarantino ; relatore Ivonne Sgura |
| Autore | Tarantino, Melissa |
| Pubbl/distr/stampa | Lecce : Università del Salento. Dipartimento di Matematica e Fisica "Ennio De Giorgi". Corso di Laurea magistrale in Matematica, a.a. 2017-18 |
| Descrizione fisica | 69 p. ; 30 cm |
| Altri autori (Persone) | Sgura, Ivonne |
| Soggetto topico |
Reaction-diffusion equations
Sobolev spaces Partial differential equations Finite difference methods |
| Classificazione |
AMS 35K57
AMS 65M06 AMS 65M12 AMS 65M20 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Record Nr. | UNISALENTO-991003677079707536 |
Tarantino, Melissa
|
||
| Lecce : Università del Salento. Dipartimento di Matematica e Fisica "Ennio De Giorgi". Corso di Laurea magistrale in Matematica, a.a. 2017-18 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski
| Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski |
| Autore | Grzybowski Bartosz A |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, 2009 |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 541.39 |
| Soggetto topico |
Reaction mechanisms (Chemistry)
Reaction-diffusion equations Microtechnology - Mathematics Nanotechnology - Mathematics |
| ISBN |
1-282-13814-6
9786612138140 0-470-74162-7 0-470-74163-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology; Contents; Preface; List of Boxed Examples; 1 Panta Rei: Everything Flows; 1.1 HISTORICAL PERSPECTIVE; 1.2 WHAT LIES AHEAD?; 1.3 HOW NATURE USES RD; 1.3.1 Animate Systems; 1.3.2 Inanimate Systems; 1.4 RD IN SCIENCE AND TECHNOLOGY; REFERENCES; 2 Basic Ingredients: Diffusion; 2.1 DIFFUSION EQUATION; 2.2 SOLVING DIFFUSION EQUATIONS; 2.2.1 Separation of Variables; 2.2.2 Laplace Transforms; 2.3 THE USE OF SYMMETRY AND SUPERPOSITION; 2.4 CYLINDRICAL AND SPHERICAL COORDINATES; 2.5 ADVANCED TOPICS; REFERENCES
3 Chemical Reactions3.1 REACTIONS AND RATES; 3.2 CHEMICAL EQUILIBRIUM; 3.3 IONIC REACTIONS AND SOLUBILITY PRODUCTS; 3.4 AUTOCATALYSIS, COOPERATIVITY AND FEEDBACK; 3.5 OSCILLATING REACTIONS; 3.6 REACTIONS IN GELS; REFERENCES; 4 Putting It All Together: Reaction-Diffusion Equations and the Methods of Solving Them; 4.1 GENERAL FORM OF REACTION-DIFFUSION EQUATIONS; 4.2 RD EQUATIONS THAT CAN BE SOLVED ANALYTICALLY; 4.3 SPATIAL DISCRETIZATION; 4.3.1 Finite Difference Methods; 4.3.2 Finite Element Methods; 4.4 TEMPORAL DISCRETIZATION AND INTEGRATION; 4.4.1 Case 1: tRxn > tDiff 4.4.1.1 Forward time centered space (FTCS) differencing4.4.1.2 Backward time centered space (BTCS) differencing; 4.4.1.3 Crank-Nicholson method; 4.4.1.4 Alternating direction implicit method in two and three dimensions; 4.4.2 Case 2: tRxn << tDiff; 4.4.2.1 Operator splitting method; 4.4.2.2 Method of lines; 4.4.3 Dealing with Precipitation Reactions; 4.5 HEURISTIC RULES FOR SELECTING A NUMERICAL METHOD; 4.6 MESOSCOPIC MODELS; REFERENCES; 5 Spatial Control of Reaction-Diffusion at Small Scales: Wet Stamping (WETS); 5.1 CHOICE OF GELS; 5.2 FABRICATION APPENDIX 5A: PRACTICAL GUIDE TO MAKING AGAROSE STAMPS5A.1 PDMS Molding; 5A.2 Agarose Molding; REFERENCES; 6 Fabrication by Reaction-Diffusion: Curvilinear Microstructures for Optics and Fluidics; 6.1 MICROFABRICATION: THE SIMPLE AND THE DIFFICULT; 6.2 FABRICATING ARRAYS OF MICROLENSES BY RD AND WETS; 6.3 INTERMEZZO: SOME THOUGHTS ON RATIONAL DESIGN; 6.4 GUIDING MICROLENS FABRICATION BY LATTICE GAS MODELING; 6.5 DISJOINT FEATURES AND MICROFABRICATION OF MULTILEVEL STRUCTURES; 6.6 MICROFABRICATION OF MICROFLUIDIC DEVICES; 6.7 SHORT SUMMARY; REFERENCES 7 Multitasking: Microand Nanofabrication with Periodic Precipitation7.1 PERIODIC PRECIPITATION; 7.2 PHENOMENOLOGY OF PERIODIC PRECIPITATION; 7.3 GOVERNING EQUATIONS; 7.4 MICROSCOPIC PP PATTERNS IN TWO DIMENSIONS; 7.4.1 Feature Dimensions and Spacing; 7.4.2 Gel Thickness; 7.4.3 Degree of Gel Crosslinking; 7.4.4 Concentration of the Outer and Inner Electrolytes; 7.5 TWO-DIMENSIONAL PATTERNS FOR DIFFRACTIVE OPTICS; 7.6 BUCKLING INTO THE THIRD DIMENSION: PERIODIC 'NANOWRINKLES'; 7.7 TOWARD THE APPLICATIONS OF BUCKLED SURFACES; 7.8 PARALLEL REACTIONS AND THE NANOSCALE; REFERENCES 8 Reaction-Diffusion at Interfaces: Structuring Solid Materials |
| Record Nr. | UNINA-9910146148703321 |
|
Grzybowski Bartosz A
|
||
| Hoboken, NJ, : Wiley, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski
| Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski |
| Autore | Grzybowski Bartosz A |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, 2009 |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 541.39 |
| Soggetto topico |
Reaction mechanisms (Chemistry)
Reaction-diffusion equations Microtechnology - Mathematics Nanotechnology - Mathematics |
| ISBN |
1-282-13814-6
9786612138140 0-470-74162-7 0-470-74163-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology; Contents; Preface; List of Boxed Examples; 1 Panta Rei: Everything Flows; 1.1 HISTORICAL PERSPECTIVE; 1.2 WHAT LIES AHEAD?; 1.3 HOW NATURE USES RD; 1.3.1 Animate Systems; 1.3.2 Inanimate Systems; 1.4 RD IN SCIENCE AND TECHNOLOGY; REFERENCES; 2 Basic Ingredients: Diffusion; 2.1 DIFFUSION EQUATION; 2.2 SOLVING DIFFUSION EQUATIONS; 2.2.1 Separation of Variables; 2.2.2 Laplace Transforms; 2.3 THE USE OF SYMMETRY AND SUPERPOSITION; 2.4 CYLINDRICAL AND SPHERICAL COORDINATES; 2.5 ADVANCED TOPICS; REFERENCES
3 Chemical Reactions3.1 REACTIONS AND RATES; 3.2 CHEMICAL EQUILIBRIUM; 3.3 IONIC REACTIONS AND SOLUBILITY PRODUCTS; 3.4 AUTOCATALYSIS, COOPERATIVITY AND FEEDBACK; 3.5 OSCILLATING REACTIONS; 3.6 REACTIONS IN GELS; REFERENCES; 4 Putting It All Together: Reaction-Diffusion Equations and the Methods of Solving Them; 4.1 GENERAL FORM OF REACTION-DIFFUSION EQUATIONS; 4.2 RD EQUATIONS THAT CAN BE SOLVED ANALYTICALLY; 4.3 SPATIAL DISCRETIZATION; 4.3.1 Finite Difference Methods; 4.3.2 Finite Element Methods; 4.4 TEMPORAL DISCRETIZATION AND INTEGRATION; 4.4.1 Case 1: tRxn > tDiff 4.4.1.1 Forward time centered space (FTCS) differencing4.4.1.2 Backward time centered space (BTCS) differencing; 4.4.1.3 Crank-Nicholson method; 4.4.1.4 Alternating direction implicit method in two and three dimensions; 4.4.2 Case 2: tRxn << tDiff; 4.4.2.1 Operator splitting method; 4.4.2.2 Method of lines; 4.4.3 Dealing with Precipitation Reactions; 4.5 HEURISTIC RULES FOR SELECTING A NUMERICAL METHOD; 4.6 MESOSCOPIC MODELS; REFERENCES; 5 Spatial Control of Reaction-Diffusion at Small Scales: Wet Stamping (WETS); 5.1 CHOICE OF GELS; 5.2 FABRICATION APPENDIX 5A: PRACTICAL GUIDE TO MAKING AGAROSE STAMPS5A.1 PDMS Molding; 5A.2 Agarose Molding; REFERENCES; 6 Fabrication by Reaction-Diffusion: Curvilinear Microstructures for Optics and Fluidics; 6.1 MICROFABRICATION: THE SIMPLE AND THE DIFFICULT; 6.2 FABRICATING ARRAYS OF MICROLENSES BY RD AND WETS; 6.3 INTERMEZZO: SOME THOUGHTS ON RATIONAL DESIGN; 6.4 GUIDING MICROLENS FABRICATION BY LATTICE GAS MODELING; 6.5 DISJOINT FEATURES AND MICROFABRICATION OF MULTILEVEL STRUCTURES; 6.6 MICROFABRICATION OF MICROFLUIDIC DEVICES; 6.7 SHORT SUMMARY; REFERENCES 7 Multitasking: Microand Nanofabrication with Periodic Precipitation7.1 PERIODIC PRECIPITATION; 7.2 PHENOMENOLOGY OF PERIODIC PRECIPITATION; 7.3 GOVERNING EQUATIONS; 7.4 MICROSCOPIC PP PATTERNS IN TWO DIMENSIONS; 7.4.1 Feature Dimensions and Spacing; 7.4.2 Gel Thickness; 7.4.3 Degree of Gel Crosslinking; 7.4.4 Concentration of the Outer and Inner Electrolytes; 7.5 TWO-DIMENSIONAL PATTERNS FOR DIFFRACTIVE OPTICS; 7.6 BUCKLING INTO THE THIRD DIMENSION: PERIODIC 'NANOWRINKLES'; 7.7 TOWARD THE APPLICATIONS OF BUCKLED SURFACES; 7.8 PARALLEL REACTIONS AND THE NANOSCALE; REFERENCES 8 Reaction-Diffusion at Interfaces: Structuring Solid Materials |
| Record Nr. | UNINA-9910830644303321 |
|
Grzybowski Bartosz A
|
||
| Hoboken, NJ, : Wiley, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski
| Chemistry in motion [[electronic resource] ] : reaction-diffusion systems for micro- and nanotechnology / / Bartosz A. Grzybowski |
| Autore | Grzybowski Bartosz A |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, 2009 |
| Descrizione fisica | 1 online resource (304 p.) |
| Disciplina | 541.39 |
| Soggetto topico |
Reaction mechanisms (Chemistry)
Reaction-diffusion equations Microtechnology - Mathematics Nanotechnology - Mathematics |
| ISBN |
1-282-13814-6
9786612138140 0-470-74162-7 0-470-74163-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology; Contents; Preface; List of Boxed Examples; 1 Panta Rei: Everything Flows; 1.1 HISTORICAL PERSPECTIVE; 1.2 WHAT LIES AHEAD?; 1.3 HOW NATURE USES RD; 1.3.1 Animate Systems; 1.3.2 Inanimate Systems; 1.4 RD IN SCIENCE AND TECHNOLOGY; REFERENCES; 2 Basic Ingredients: Diffusion; 2.1 DIFFUSION EQUATION; 2.2 SOLVING DIFFUSION EQUATIONS; 2.2.1 Separation of Variables; 2.2.2 Laplace Transforms; 2.3 THE USE OF SYMMETRY AND SUPERPOSITION; 2.4 CYLINDRICAL AND SPHERICAL COORDINATES; 2.5 ADVANCED TOPICS; REFERENCES
3 Chemical Reactions3.1 REACTIONS AND RATES; 3.2 CHEMICAL EQUILIBRIUM; 3.3 IONIC REACTIONS AND SOLUBILITY PRODUCTS; 3.4 AUTOCATALYSIS, COOPERATIVITY AND FEEDBACK; 3.5 OSCILLATING REACTIONS; 3.6 REACTIONS IN GELS; REFERENCES; 4 Putting It All Together: Reaction-Diffusion Equations and the Methods of Solving Them; 4.1 GENERAL FORM OF REACTION-DIFFUSION EQUATIONS; 4.2 RD EQUATIONS THAT CAN BE SOLVED ANALYTICALLY; 4.3 SPATIAL DISCRETIZATION; 4.3.1 Finite Difference Methods; 4.3.2 Finite Element Methods; 4.4 TEMPORAL DISCRETIZATION AND INTEGRATION; 4.4.1 Case 1: tRxn > tDiff 4.4.1.1 Forward time centered space (FTCS) differencing4.4.1.2 Backward time centered space (BTCS) differencing; 4.4.1.3 Crank-Nicholson method; 4.4.1.4 Alternating direction implicit method in two and three dimensions; 4.4.2 Case 2: tRxn << tDiff; 4.4.2.1 Operator splitting method; 4.4.2.2 Method of lines; 4.4.3 Dealing with Precipitation Reactions; 4.5 HEURISTIC RULES FOR SELECTING A NUMERICAL METHOD; 4.6 MESOSCOPIC MODELS; REFERENCES; 5 Spatial Control of Reaction-Diffusion at Small Scales: Wet Stamping (WETS); 5.1 CHOICE OF GELS; 5.2 FABRICATION APPENDIX 5A: PRACTICAL GUIDE TO MAKING AGAROSE STAMPS5A.1 PDMS Molding; 5A.2 Agarose Molding; REFERENCES; 6 Fabrication by Reaction-Diffusion: Curvilinear Microstructures for Optics and Fluidics; 6.1 MICROFABRICATION: THE SIMPLE AND THE DIFFICULT; 6.2 FABRICATING ARRAYS OF MICROLENSES BY RD AND WETS; 6.3 INTERMEZZO: SOME THOUGHTS ON RATIONAL DESIGN; 6.4 GUIDING MICROLENS FABRICATION BY LATTICE GAS MODELING; 6.5 DISJOINT FEATURES AND MICROFABRICATION OF MULTILEVEL STRUCTURES; 6.6 MICROFABRICATION OF MICROFLUIDIC DEVICES; 6.7 SHORT SUMMARY; REFERENCES 7 Multitasking: Microand Nanofabrication with Periodic Precipitation7.1 PERIODIC PRECIPITATION; 7.2 PHENOMENOLOGY OF PERIODIC PRECIPITATION; 7.3 GOVERNING EQUATIONS; 7.4 MICROSCOPIC PP PATTERNS IN TWO DIMENSIONS; 7.4.1 Feature Dimensions and Spacing; 7.4.2 Gel Thickness; 7.4.3 Degree of Gel Crosslinking; 7.4.4 Concentration of the Outer and Inner Electrolytes; 7.5 TWO-DIMENSIONAL PATTERNS FOR DIFFRACTIVE OPTICS; 7.6 BUCKLING INTO THE THIRD DIMENSION: PERIODIC 'NANOWRINKLES'; 7.7 TOWARD THE APPLICATIONS OF BUCKLED SURFACES; 7.8 PARALLEL REACTIONS AND THE NANOSCALE; REFERENCES 8 Reaction-Diffusion at Interfaces: Structuring Solid Materials |
| Record Nr. | UNINA-9910840723703321 |
|
Grzybowski Bartosz A
|
||
| Hoboken, NJ, : Wiley, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Degenerate diffusions : initial value problems and local regularity theory / Panagiota Daskalopoulos, Carlos E. Kenig
| Degenerate diffusions : initial value problems and local regularity theory / Panagiota Daskalopoulos, Carlos E. Kenig |
| Autore | Daskalopoulos, Panagiota |
| Pubbl/distr/stampa | Zurich : European Mathematical Society, c2007 |
| Descrizione fisica | vii, 198 p.; 25 cm |
| Disciplina | 515.353 |
| Altri autori (Persone) | Kenig, Carlos E. |
| Collana | EMS tracts in mathematics ; 1 |
| Soggetto topico |
Reaction-diffusion equations
Cauchy problem Dirichlet problem Porous materials - Mathematical models |
| ISBN | 9783037190333 |
| Classificazione |
AMS 34D05
AMS 35B25 AMS 35B40 AMS 35J20 AMS 35J70 AMS 35K55 AMS 35K65 LC QA378.D37 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000292789707536 |
|
Daskalopoulos, Panagiota
|
||
| Zurich : European Mathematical Society, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
The dynamics of modulated wave trains / / Arjen Doelman [and three others]
| The dynamics of modulated wave trains / / Arjen Doelman [and three others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (122 p.) |
| Disciplina | 515.3534 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Approximation theory Burgers equation |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0540-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Notation""; ""Chapter 1. Introduction""; ""1.1. Grasshopper's guide""; ""1.2. Slowly-varying modulations of nonlinear wave trains""; ""1.3. Predictions from the Burgers equation""; ""1.4. Verifying the predictions made from the Burgers equation""; ""1.5. Related modulation equations""; ""1.6. References to related works""; ""Chapter 2. The Burgers equation""; ""2.1. Decay estimates""; ""2.2. Fronts in the Burgers equation""; ""Chapter 3. The complex cubic Ginzburg�Landau equation""; ""3.1. Set-up""; ""3.2. Slowly-varying modulations of the k = 0 wave train: Results""
""3.3. Derivation of the Burgers equation""""3.4. The construction of higher-order approximations""; ""3.5. The approximation theorem for the wave numbers""; ""3.6. Mode filters, and separation into critical and noncritical modes""; ""3.7. Estimates of the linear semigroups""; ""3.8. Estimates of the residual""; ""3.9. Estimates of the errors""; ""3.10. Proofs of the theorems from Â3.2""; ""Chapter 4. Reaction-diffusion equations: Set-up and results""; ""4.1. The abstract set-up""; ""4.2. Expansions of the linear and nonlinear dispersion relations"" ""4.3. Formal derivation of the Burgers equation""""4.4. Validity of the Burgers equation""; ""4.5. Existence and stability of weak shocks""; ""Chapter 5. Validity of the Burgers equation in reaction-diffusion equations""; ""5.1. From phases to wave numbers""; ""5.2. Bloch-wave analysis""; ""5.3. Mode filters, and separation into critical and noncritical modes""; ""5.4. Estimates for residuals and errors""; ""5.5. Proofs of the theorems from Â4.4""; ""Chapter 6. Validity of the inviscid Burgers equation in reaction-diffusion systems""; ""6.1. An illustration: The Ginzburgâ€?Landau equation"" ""6.2. Formal derivation of the conservation law""""6.3. Validity of the inviscid Burgers equation""; ""6.4. Proof of the theorems from Â6.3""; ""Chapter 7. Modulations of wave trains near sideband instabilities""; ""7.1. Introduction""; ""7.2. An illustration: The Ginzburgâ€?Landau equation""; ""7.3. Validity of the Kortewegâ€?de Vries and the Kuramotoâ€?Sivashinsky equation""; ""7.4. Proof of Theorem 7.2""; ""7.5. Proof of Theorem 7.5""; ""Chapter 8. Existence and stability of weak shocks""; ""8.1. Proof of Theorem 4.10""; ""8.2. Proof of Theorem 4.12"" ""Chapter 9. Existence of shocks in the long-wavelength limit""""9.1. A lattice model for weakly interacting pulses""; ""9.2. Proof of Theorem 9.2""; ""Chapter 10. Applications""; ""10.1. The FitzHughâ€?Nagumo equation""; ""10.2. The weakly unstable Taylorâ€?Couette problem""; ""Bibliography"" |
| Record Nr. | UNINA-9910480757103321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The dynamics of modulated wave trains / / Arjen Doelman [and three others]
| The dynamics of modulated wave trains / / Arjen Doelman [and three others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (122 p.) |
| Disciplina | 515.3534 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Approximation theory Burgers equation |
| ISBN | 1-4704-0540-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Notation""; ""Chapter 1. Introduction""; ""1.1. Grasshopper's guide""; ""1.2. Slowly-varying modulations of nonlinear wave trains""; ""1.3. Predictions from the Burgers equation""; ""1.4. Verifying the predictions made from the Burgers equation""; ""1.5. Related modulation equations""; ""1.6. References to related works""; ""Chapter 2. The Burgers equation""; ""2.1. Decay estimates""; ""2.2. Fronts in the Burgers equation""; ""Chapter 3. The complex cubic Ginzburg�Landau equation""; ""3.1. Set-up""; ""3.2. Slowly-varying modulations of the k = 0 wave train: Results""
""3.3. Derivation of the Burgers equation""""3.4. The construction of higher-order approximations""; ""3.5. The approximation theorem for the wave numbers""; ""3.6. Mode filters, and separation into critical and noncritical modes""; ""3.7. Estimates of the linear semigroups""; ""3.8. Estimates of the residual""; ""3.9. Estimates of the errors""; ""3.10. Proofs of the theorems from Â3.2""; ""Chapter 4. Reaction-diffusion equations: Set-up and results""; ""4.1. The abstract set-up""; ""4.2. Expansions of the linear and nonlinear dispersion relations"" ""4.3. Formal derivation of the Burgers equation""""4.4. Validity of the Burgers equation""; ""4.5. Existence and stability of weak shocks""; ""Chapter 5. Validity of the Burgers equation in reaction-diffusion equations""; ""5.1. From phases to wave numbers""; ""5.2. Bloch-wave analysis""; ""5.3. Mode filters, and separation into critical and noncritical modes""; ""5.4. Estimates for residuals and errors""; ""5.5. Proofs of the theorems from Â4.4""; ""Chapter 6. Validity of the inviscid Burgers equation in reaction-diffusion systems""; ""6.1. An illustration: The Ginzburgâ€?Landau equation"" ""6.2. Formal derivation of the conservation law""""6.3. Validity of the inviscid Burgers equation""; ""6.4. Proof of the theorems from Â6.3""; ""Chapter 7. Modulations of wave trains near sideband instabilities""; ""7.1. Introduction""; ""7.2. An illustration: The Ginzburgâ€?Landau equation""; ""7.3. Validity of the Kortewegâ€?de Vries and the Kuramotoâ€?Sivashinsky equation""; ""7.4. Proof of Theorem 7.2""; ""7.5. Proof of Theorem 7.5""; ""Chapter 8. Existence and stability of weak shocks""; ""8.1. Proof of Theorem 4.10""; ""8.2. Proof of Theorem 4.12"" ""Chapter 9. Existence of shocks in the long-wavelength limit""""9.1. A lattice model for weakly interacting pulses""; ""9.2. Proof of Theorem 9.2""; ""Chapter 10. Applications""; ""10.1. The FitzHughâ€?Nagumo equation""; ""10.2. The weakly unstable Taylorâ€?Couette problem""; ""Bibliography"" |
| Record Nr. | UNINA-9910788854903321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The dynamics of modulated wave trains / / Arjen Doelman [and three others]
| The dynamics of modulated wave trains / / Arjen Doelman [and three others] |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (122 p.) |
| Disciplina | 515.3534 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Approximation theory Burgers equation |
| ISBN | 1-4704-0540-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Notation""; ""Chapter 1. Introduction""; ""1.1. Grasshopper's guide""; ""1.2. Slowly-varying modulations of nonlinear wave trains""; ""1.3. Predictions from the Burgers equation""; ""1.4. Verifying the predictions made from the Burgers equation""; ""1.5. Related modulation equations""; ""1.6. References to related works""; ""Chapter 2. The Burgers equation""; ""2.1. Decay estimates""; ""2.2. Fronts in the Burgers equation""; ""Chapter 3. The complex cubic Ginzburg�Landau equation""; ""3.1. Set-up""; ""3.2. Slowly-varying modulations of the k = 0 wave train: Results""
""3.3. Derivation of the Burgers equation""""3.4. The construction of higher-order approximations""; ""3.5. The approximation theorem for the wave numbers""; ""3.6. Mode filters, and separation into critical and noncritical modes""; ""3.7. Estimates of the linear semigroups""; ""3.8. Estimates of the residual""; ""3.9. Estimates of the errors""; ""3.10. Proofs of the theorems from Â3.2""; ""Chapter 4. Reaction-diffusion equations: Set-up and results""; ""4.1. The abstract set-up""; ""4.2. Expansions of the linear and nonlinear dispersion relations"" ""4.3. Formal derivation of the Burgers equation""""4.4. Validity of the Burgers equation""; ""4.5. Existence and stability of weak shocks""; ""Chapter 5. Validity of the Burgers equation in reaction-diffusion equations""; ""5.1. From phases to wave numbers""; ""5.2. Bloch-wave analysis""; ""5.3. Mode filters, and separation into critical and noncritical modes""; ""5.4. Estimates for residuals and errors""; ""5.5. Proofs of the theorems from Â4.4""; ""Chapter 6. Validity of the inviscid Burgers equation in reaction-diffusion systems""; ""6.1. An illustration: The Ginzburgâ€?Landau equation"" ""6.2. Formal derivation of the conservation law""""6.3. Validity of the inviscid Burgers equation""; ""6.4. Proof of the theorems from Â6.3""; ""Chapter 7. Modulations of wave trains near sideband instabilities""; ""7.1. Introduction""; ""7.2. An illustration: The Ginzburgâ€?Landau equation""; ""7.3. Validity of the Kortewegâ€?de Vries and the Kuramotoâ€?Sivashinsky equation""; ""7.4. Proof of Theorem 7.2""; ""7.5. Proof of Theorem 7.5""; ""Chapter 8. Existence and stability of weak shocks""; ""8.1. Proof of Theorem 4.10""; ""8.2. Proof of Theorem 4.12"" ""Chapter 9. Existence of shocks in the long-wavelength limit""""9.1. A lattice model for weakly interacting pulses""; ""9.2. Proof of Theorem 9.2""; ""Chapter 10. Applications""; ""10.1. The FitzHughâ€?Nagumo equation""; ""10.2. The weakly unstable Taylorâ€?Couette problem""; ""Bibliography"" |
| Record Nr. | UNINA-9910829176903321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Entire solutions of semilinear elliptic equations / I. Kuzin, S. Pohozaev
| Entire solutions of semilinear elliptic equations / I. Kuzin, S. Pohozaev |
| Autore | Kuzin, Ilja A. |
| Pubbl/distr/stampa | Basel ; Boston ; Berlin : Birkhäuser, c1997 |
| Descrizione fisica | vi, 250 p. : ill. ; 24 cm. |
| Disciplina | 515.355 |
| Altri autori (Persone) | Pokhozhaev, S. I. |
| Collana | Progress in nonlinear differential equations and their applications ; 33 |
| Soggetto topico |
Elliptic differential equations
Mathematical physics Reaction-diffusion equations |
| ISBN | 3764353236 |
| Classificazione | AMS 35J60 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | en |
| Record Nr. | UNISALENTO-991000862279707536 |
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Kuzin, Ilja A.
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| Basel ; Boston ; Berlin : Birkhäuser, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Numerical analysis and reaction-diffusion equations""; ""1.2. The limitations of classic a priori error analysis""; ""1.3. What we do and don't do in this paper""; ""1.4. A brief overview of related work""; ""1.5. The plan of the paper""; ""Acknowledgments""; ""Chapter 2. A framework for a posteriori error estimation""; ""2.1. The continuous problem and its discretization""; ""2.2. The residual error""; ""2.3. The dual problem and a formula for the error""; ""2.4. The stability factors and the a posteriori error estimate""
""Chapter 3. The size of the residual errors and stability factors""""3.1. The size of the residual errors""; ""3.2. The size of the stability factors""; ""3.3. Application of the analysis to systems with constant diffusion""; ""3.4. The a posteriori estimate and convergence""; ""Chapter 4. Computational error estimation""; ""4.1. Two examples and a stability factor gallery""; ""4.2. Choosing data for the dual problem""; ""4.3. Linearization and the approximate dual problem""; ""4.4. A test of the accuracy and reliability of the error estimate""; ""4.5. Some details of implementation"" ""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography"" |
| Record Nr. | UNINA-9910480413403321 |
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Estep Donald J. <1959->
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| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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