Compactness methods for nonlinear evolutions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman [u.a.]
1995
|
| Edition: | 2. ed. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
75 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 241 S. graph. Darst. |
| ISBN: | 0582248728 |
Staff View
MARC
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| 245 | 1 | 0 | |a Compactness methods for nonlinear evolutions |c I. I. Vrabie |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Harlow |b Longman [u.a.] |c 1995 | |
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Record in the Search Index
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| adam_text | Contents
Foreword ix
Preface xi
Preface to the Second Edition xiii
Notation and Conventions xv
1 Elements of Nonlinear Functional Analysis 1
1.1 Inequalities 2
1.2 Basic Compactness Results 3
1.3 Compactness in Some Function Spaces 7
1.4 Semi inner Products 10
1.5 Accretive Operators 15
1.6 Subdifferentials 20
1.7 Evolutions Governed by Accretive Operators 22
1.8 Nonlinear Semigroups 28
1.9 Existence of Strong Solutions 30
1.10 Generalized Gradients 32
2 Fundamental Compactness Results 33
2.1 How S(t) and J Behave for Small t and A. Brezis Theorem 33
2.2 Compact Semigroups 36
2.3 Compact Subsets of Solutions in C([a, 6];X) 44
2.4 The Compact Resolvent Case 52
2.5 The Equicontinuous Semigroup Case 57
2.6 Compact Subsets of Solutions in Lp([a, ];X) 65
2.7 The Nonlinear Diffusion Equation 70
2.8 Applications to the Pseudo Laplace Operator 75
2.9 Applications to Optimal Control Theory 78
3 Nonlinear Perturbations of Accretive Operators 85
3.1 Preliminaries on Multivalued Mappings 85
3.2 Continuation of the Solutions 91
3.3 Multivalued Perturbations 98
3.4 Applications to Reaction Diffusion Systems 106
vii
viii Contents
3.5 Applications to Closed Loop Systems 114
3.6 Compact Perturbations 118
3.7 Applications to the Nonlinear Wave Equation 125
3.8 Single Valued Perturbations 131
3.9 The Nonlinear Perturbed Diffusion Equation 137
3.10 PDEs Governed by the p Laplace Operator 140
4 Demiclosed Perturbations of Subdifferentials 145
4.1 Statement of the Problem 145
4.2 The Smooth Initial Datum Case 147
4.3 The Nonsmooth Initial Datum Case 152
4.4 Nonlinear Interpolation Classes 157
4.5 Quasi Autonomous Equations 165
4.6 The Intermediate Initial Datum Case 168
4.7 Continuation of the Solutions 172
4.8 The Case of Small Data 176
4.9 A Class of Nonlinear Parabolic Equations 181
4.10 Applications to the Navier Stokes Equations 189
5 Functional and Integrodifferential Equations 195
5.1 A Class of Volterra Integrodifferential Equations 195
5.2 The 4 Demiclosed Integrand Case 200
5.3 A Class of Functional Differential Equations 208
5.4 Heat Conduction in Materials with Memory 213
5.5 The Vibrations of a String with Memory 218
Bibliographical Notes, Comments and Open Problems 221
References 229
Index 240
|
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| indexdate | 2024-07-09T17:53:11Z |
| institution | BVB |
| isbn | 0582248728 |
| language | English |
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| physical | XVI, 241 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Longman [u.a.] |
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| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Vrabie, Ioan I. Verfasser aut Compactness methods for nonlinear evolutions I. I. Vrabie 2. ed. Harlow Longman [u.a.] 1995 XVI, 241 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 75 Équations d'évolution non linéaires ram Evolution equations, Nonlinear Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s DE-604 Pitman monographs and surveys in pure and applied mathematics 75 (DE-604)BV000022446 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006982556&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vrabie, Ioan I. Compactness methods for nonlinear evolutions Pitman monographs and surveys in pure and applied mathematics Équations d'évolution non linéaires ram Evolution equations, Nonlinear Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| subject_GND | (DE-588)4221363-0 |
| title | Compactness methods for nonlinear evolutions |
| title_auth | Compactness methods for nonlinear evolutions |
| title_exact_search | Compactness methods for nonlinear evolutions |
| title_full | Compactness methods for nonlinear evolutions I. I. Vrabie |
| title_fullStr | Compactness methods for nonlinear evolutions I. I. Vrabie |
| title_full_unstemmed | Compactness methods for nonlinear evolutions I. I. Vrabie |
| title_short | Compactness methods for nonlinear evolutions |
| title_sort | compactness methods for nonlinear evolutions |
| topic | Équations d'évolution non linéaires ram Evolution equations, Nonlinear Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| topic_facet | Équations d'évolution non linéaires Evolution equations, Nonlinear Nichtlineare Evolutionsgleichung |
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