Linear and quasi-linear evolution equations in Hilbert spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2012
|
| Schriftenreihe: | Graduate studies in mathematics
135 |
| Schlagworte: |
Partial differential equations
> Hyperbolic equations and systems
> Initial value problems for second-order hyperbolic equations
Partial differential equations
> Hyperbolic equations and systems
> Quasilinear second-order hyperbolic equations
Partial differential equations
> Parabolic equations and systems
> Initial value problems for second-order parabolic equations
Partial differential equations
> Equations of mathematical physics and other areas of application
> Maxwell equations
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 377 S. |
| ISBN: | 9780821875766 |
Internformat
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| 245 | 1 | 0 | |a Linear and quasi-linear evolution equations in Hilbert spaces |c Pascal Cherrier ; Albert Milani |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2012 | |
| 300 | |a XVIII, 377 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 135 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Initial value problems | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Hilbert space | |
| 650 | 7 | |a Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations |2 msc | |
| 650 | 7 | |a Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids |2 msc | |
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Datensatz im Suchindex
| _version_ | 1804149427376488448 |
|---|---|
| adam_text | Titel: Linear and quasi-linear evolution equations in Hilbert spaces
Autor: Cherrier, Pascal
Jahr: 2012
Contents
Preface
ix
Chapter 1. Punctional Framework 1
§1.1. Basic Notation 1
§1.2. Functional Analysis Results 4
§1.3. Holder Spaces 7
§1.4. Lebesgue Spaces 9
§1.5. Sobolev Spaces 13
§1.6. Orthogonal Bases in Hm(RN) 51
§1.7. Sobolev Spaces Involving Time 60
Chapter 2. Linear Equations 77
§2.1. Introduction 77
§2.2. The Hyperbolic Cauchy Problem 78
§2.3. Proof of Theorem 2.2.1 81
§2.4. Weak Solutions 104
§2.5. The Parabolic Cauchy Problem 107
Chapter 3. Quasi-linear Equations 119
§3.1. Introduction 119
§3.2. The Hyperbolic Cauchy Problem 122
§3.3. Proof of Theorem 3.2.1 131
§3.4. The Parabolic Cauchy Problem 145
vn
viii Contents
Chapter 4. Global Existence 153
§4.1. Introduction 153
§4.2. Life Span of Solutions 155
§4.3. Non Dissipative Finite Time Blow-Up 159
§4.4. Almost Global Existence 171
§4.5. Global Existence for Dissipative Equations 175
§4.6. The Parabolic Problem 214
Chapter 5. Asymptotic Behavior 233
§5.1. Introduction 233
§5.2. Convergence «^(t) - txsta 234
§5.3. Convergence vPar(t) - • wsta 241
§5.4. Stability Estimates 244
§5.5. The Diffusion Phenomenon 278
Chapter 6. Singular Convergence 293
§6.1. Introduction 293
§6.2. An Example from ODEs 295
§6.3. Uniformly Local and Global Existence 301
§6.4. Singular Perturbation 305
§6.5. Almost Global Existence 326
Chapter 7. Maxwell and von Karman Equations 335
§7.1. Maxwell s Equations 335
§7.2. von Karman s Equations 343
List of Function Spaces 361
Bibliography 365
Index 375
|
| any_adam_object | 1 |
| author | Cherrier, Pascal 1950- |
| author_GND | (DE-588)1025880838 (DE-588)1027129056 |
| author_facet | Cherrier, Pascal 1950- |
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| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)809153452 (DE-599)BVBBV040384160 |
| dewey-full | 515/.733 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.733 |
| dewey-search | 515/.733 |
| dewey-sort | 3515 3733 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T00:22:51Z |
| institution | BVB |
| isbn | 9780821875766 |
| language | English |
| lccn | 2012002958 |
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| physical | XVIII, 377 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Cherrier, Pascal 1950- Verfasser (DE-588)1025880838 aut Linear and quasi-linear evolution equations in Hilbert spaces Pascal Cherrier ; Albert Milani Providence, RI American Mathematical Society 2012 XVIII, 377 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 135 Includes bibliographical references and index Initial value problems Differential equations, Hyperbolic Evolution equations Hilbert space Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations msc Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations msc Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations msc Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids msc Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 s Hyperbolische Differentialgleichung (DE-588)4131213-2 s Parabolische Differentialgleichung (DE-588)4173245-5 s Evolutionsgleichung (DE-588)4129061-6 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Milani, Albert Sonstige (DE-588)1027129056 oth Graduate studies in mathematics 135 (DE-604)BV009739289 135 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cherrier, Pascal 1950- Linear and quasi-linear evolution equations in Hilbert spaces Graduate studies in mathematics Initial value problems Differential equations, Hyperbolic Evolution equations Hilbert space Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations msc Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations msc Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations msc Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids msc Evolutionsgleichung (DE-588)4129061-6 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Anfangswertproblem (DE-588)4001991-3 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4131213-2 (DE-588)4159850-7 (DE-588)4001991-3 (DE-588)4173245-5 |
| title | Linear and quasi-linear evolution equations in Hilbert spaces |
| title_auth | Linear and quasi-linear evolution equations in Hilbert spaces |
| title_exact_search | Linear and quasi-linear evolution equations in Hilbert spaces |
| title_full | Linear and quasi-linear evolution equations in Hilbert spaces Pascal Cherrier ; Albert Milani |
| title_fullStr | Linear and quasi-linear evolution equations in Hilbert spaces Pascal Cherrier ; Albert Milani |
| title_full_unstemmed | Linear and quasi-linear evolution equations in Hilbert spaces Pascal Cherrier ; Albert Milani |
| title_short | Linear and quasi-linear evolution equations in Hilbert spaces |
| title_sort | linear and quasi linear evolution equations in hilbert spaces |
| topic | Initial value problems Differential equations, Hyperbolic Evolution equations Hilbert space Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations msc Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations msc Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations msc Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations msc Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids msc Evolutionsgleichung (DE-588)4129061-6 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Anfangswertproblem (DE-588)4001991-3 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Initial value problems Differential equations, Hyperbolic Evolution equations Hilbert space Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids Evolutionsgleichung Hyperbolische Differentialgleichung Hilbert-Raum Anfangswertproblem Parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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