Asymptotic issues for some partial differential equations:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | ix, 252 Seiten |
| ISBN: | 9781783268917 |
Staff View
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| 245 | 1 | 0 | |a Asymptotic issues for some partial differential equations |c Michel Marie Chipot (University of Zurich, Switzerland) |
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Record in the Search Index
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| adam_text | Contents
4
Foreword v
1. Introduction 1
1.1 The Dirichlet problem...................................... 1
1.2 Periodic problems.......................................... 6
1.3 Problems in unbounded domains.............................. 9
1.4 Rescaling ................................................ 11
1.5 Eigenvalue problems....................................... 12
1.6 Calculus of variations problems........................... 15
1.7 Parabolic problems........................................ 19
1.8 Strongly nonlinear problems............................... 24
1.9 Higher order operators.................................... 29
1.10 Higher order estimates.................................... 33
1.11 Global convergence........................................ 35
1.12 Correctors for the Dirichlet problem...................... 37
2. The Dirichlet problem in some unbounded domains 47
2.1 The linear case........................................... 47
2.2 A quasilinear case........................................ 55
2.3 Pointwise convergence..................................... 64
3. The pure Neumann problem 71
3.1 Introduction.............................................. 71
3.2 Construction of a solution to the pure Neumann
problem................................................... 76
3.3 The case of data independent of x ........................ 87
3.4 The case with a lower order term.......................... 92
vii
viii Asymptotic Issues for Some Partial Differential Equations
4. Periodic problems 101
4.1 A general theory.......................................... 101
4.2 Some degenerate case...................................... 110
4.3 Application to the periodic obstacle problem.............. 113
5. Anisotropic singular perturbation problems 119
5.1 Introduction.............................................. 119
5.2 Anisotropic singular perturbation problems................ 122
5.3 Estimates for the rate of convergence..................... 130
6. Eigenvalue problems 133
6.1 Introduction.............................................. 133
6.2 Convergence of the eigenvalues............................ 134
6.3 Convergence of the eigenfunctions......................... 144
6.4 An application ........................................... 150
6.5 The case of Neumann boundary conditions................... 155
7. Elliptic systems 165
7.1 Abstract formulation...................................... 165
7.2 Some applications......................................... 169
8. The Stokes problem 177
8.1 Introduction and notation................................. 177
8.2 Auxiliary lemmas.......................................... 179
8.3 Main results.............................................. 181
9. Variational inequalities 191
9.1 A simple result........................................... 191
9.2 The obstacle problem in unbounded domains.............. 194
9.3 A general framework....................................... 205
9.4 Some applications......................................... 211
10. Calculus of variations 213
10.1 Monotonicity properties....................................213
10.2 A convergence result...................................... 217
10.3 The case of the ¿/-Laplace operator....................... 230
Some concluding remarks 237
Contents ix
Appendix A 239
A.l Dictionary of the main notation........................... 239
A.2 Some existence results.................................... 240
A.3 Poincare’s Inequality..................................... 243
Bibliography 245
Index 251
Asymptotic Issues for Some Partial Differential Equations
Much progress has been made in recent years on the issue of asymptotic
behavior of problems set in cylinders. This book goes one step further by
presenting the latest accomplishments on asymptotic behavior in domains
which become unbounded.
It also investigates new issues which have emerged including existence
and uniqueness of solution in unbounded domains, anisotropic singular
perturbations, periodic behavior forced by periodic data. These new advances
are treated with original techniques developed to investigate the asymptotic
behavior of various problems.
Theories investigated throughout the book can be applied to other problems
related to partial differential equations, making it an important text for students
and researchers within the discipline.
Asymptotic Issues for Some Partial Differential Equations is an updated account
of t Goes to Plus Infinity, published by Birkhauser in 2002.
Imperial College Press
P1064 he
ISBN 978-1-78326-891-7
7
781783 26891
www.icpress.co.uk
9
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| spelling | Chipot, Michel 1949- Verfasser (DE-588)110320999 aut Asymptotic issues for some partial differential equations Michel Marie Chipot (University of Zurich, Switzerland) London Imperial College Press [2016] ix, 252 Seiten txt rdacontent n rdamedia nc rdacarrier Differential equations, Partial Asymptotic theory Differential equations Asymptotic theory Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s DE-604 Erscheint auch als Online-Ausgabe 10.1142/9781783268924 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132158&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132158&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Chipot, Michel 1949- Asymptotic issues for some partial differential equations Differential equations, Partial Asymptotic theory Differential equations Asymptotic theory Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4134367-0 (DE-588)4044779-0 |
| title | Asymptotic issues for some partial differential equations |
| title_auth | Asymptotic issues for some partial differential equations |
| title_exact_search | Asymptotic issues for some partial differential equations |
| title_full | Asymptotic issues for some partial differential equations Michel Marie Chipot (University of Zurich, Switzerland) |
| title_fullStr | Asymptotic issues for some partial differential equations Michel Marie Chipot (University of Zurich, Switzerland) |
| title_full_unstemmed | Asymptotic issues for some partial differential equations Michel Marie Chipot (University of Zurich, Switzerland) |
| title_short | Asymptotic issues for some partial differential equations |
| title_sort | asymptotic issues for some partial differential equations |
| topic | Differential equations, Partial Asymptotic theory Differential equations Asymptotic theory Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Asymptotic theory Differential equations Asymptotic theory Asymptotisches Lösungsverhalten Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132158&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030132158&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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