G-convergence and homogenization of nonlinear partial differential operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1997
|
| Schriftenreihe: | Mathematics and its applications
422 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 249 S. |
| ISBN: | 079234720X |
Internformat
MARC
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| 100 | 1 | |a Pankov, Aleksandr A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a G-convergence and homogenization of nonlinear partial differential operators |c by Alexander Pankov |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a XIII, 249 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 422 | |
| 650 | 4 | |a Convergence opérateur | |
| 650 | 7 | |a Homogénéisation (équations différentielles) |2 ram | |
| 650 | 4 | |a Homogénéisation opérateur elliptique | |
| 650 | 7 | |a Lie, Groupes de |2 ram | |
| 650 | 4 | |a Opérateur elliptique non linéaire | |
| 650 | 4 | |a Opérateur parabolique non linéaire | |
| 650 | 7 | |a Opérateurs monotones |2 ram | |
| 650 | 4 | |a Convergence | |
| 650 | 4 | |a Homogenization (Differential equations) | |
| 650 | 4 | |a Nonlinear partial differential operators | |
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| 650 | 0 | 7 | |a Homogenisierung |g Mathematik |0 (DE-588)4403079-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlinearer partieller Differentialoperator |0 (DE-588)4171764-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127588138876928 |
|---|---|
| adam_text | Table of Contents
Preface ix
Notations xiii
1 G convergence of Abstract Operators 1
1.1 Preliminaries 1
1.1.1 Multivalued Monotone Operators 1
1.1.2 Single Valued Operators of Monotone Type 5
1.1.3 Convergence in the Sense of Kuratowski 8
1.2 G convergence of Monotone Operators 10
1.2.1 Classes of Operators 10
1.2.2 G convergence and G compactness 14
1.2.3 Comparision of Different Types of Operator Convergence ... 18
1.2.4 Some Special Propeties of G convergence 24
1.3 G convergence of Abstract Parabolic Operators 25
1.3.1 Abstract Parabolic Operators 25
1.3.2 G compactness 33
1.3.3 Properties of G convergence , 36
1.3.4 Time Homogenization of Abstract Parabolic Operators .... 41
Comments 44
2 Strong G convergence of Nonlinear Elliptic Operators 45
2.1 Nonlinear Elliptic Operators 45
2.1.1 Measurable Multivalued Functions 45
2.1.2 Multivalued Monotone Elliptic Operators 49
2.1.3 Some Classes of Single Valued Elliptic Operators 58
2.2 Strong G convergence for Multivalued Elliptic Operators 62
2.2.1 Definition of Strong G convergence 62
2.2.2 Strong G compactness 65
2.2.3 Additional Results 68
2.2.4 Variational Problems 76
2.2.5 Other Boundary Conditions 80
2.3 Strong G convergence for Single Valued Elliptic Operators 83
v
vi TABLE OF CONTENTS
2.3.1 Main Results 83
2.3.2 Proofs of Main Results: Particular Case 88
2.3.3 Proofs of Main Results: General Case 98
2.4 Further Results on Strong G convergence 108
2.4.1 Criteria for Strong G convergenvce 108
2.4.2 Stability and Comparison Results 112
2.4.3 One Dimentional Case 118
2.5 Strong Nonlinearity in Lower Order Term 120
Comments 129
3 Homogenization of Elliptic Operators 131
3.1 Random Homogeneous Fields 131
3.1.1 Definitions and Main Properties 131
3.1.2 Vector Fields and Compensated Compactness 136
3.1.3 Random Vector Fields . 137
3.2 Homogenization of Random Elliptic Operators 141
3.2.1 Multivalued Monotone Operators and Auxiliary Problem . . . 141
3.2.2 Homogenization Theorem 146
3.2.3 Properties of Homogenizated Operators 149
3.2.4 Single Valued Elliptic Operators 152
3.3 Almost Periodic Homogenization 155
3.3.1 Almost Periodic Functions 155
3.3.2 Individual Homogenization 159
3.4 One Dimentional Problems 163
3.5 Additional Results 166
3.5.1 Operators with Strong Nonlinearity 166
3.5.2 Correctors 170
Comments 172
4 Nonlinear Parabolic Operators 173
4.1 Strong G convergence 173
4.1.1 Main Definitions 173
4.1.2 Monotone Operators 177
4.1.3 General Parabolic Operators 183
4.1.4 Further Results 187
4.2 Homogenization 189
4.2.1 Setting of the Problem 189
4.2.2 Self Similar Case 192
4.2.3 Non Self Similar Cases 195
4.2.4 Spatial Homogenization 199
4.2.5 Time Homogenization • 200
4.3 An Equation of Nonstationary Filtration 203
TABLE OF CONTENTS vii
Comments 212
A Homogenization of Nonlinear Difference Schemes 213
A.I Mesh Functions . 214
A.2 G convergence 216
A.3 Homogenization 220
B Open Problems 224
References 229
Index 248
|
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| id | DE-604.BV012902643 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:35:44Z |
| institution | BVB |
| isbn | 079234720X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008781669 |
| oclc_num | 37315294 |
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| physical | XIII, 249 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Pankov, Aleksandr A. Verfasser aut G-convergence and homogenization of nonlinear partial differential operators by Alexander Pankov Dordrecht [u.a.] Kluwer 1997 XIII, 249 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 422 Convergence opérateur Homogénéisation (équations différentielles) ram Homogénéisation opérateur elliptique Lie, Groupes de ram Opérateur elliptique non linéaire Opérateur parabolique non linéaire Opérateurs monotones ram Convergence Homogenization (Differential equations) Nonlinear partial differential operators Konvergenz (DE-588)4032326-2 gnd rswk-swf Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Nichtlinearer partieller Differentialoperator (DE-588)4171764-8 gnd rswk-swf Nichtlinearer partieller Differentialoperator (DE-588)4171764-8 s Konvergenz (DE-588)4032326-2 s DE-604 Homogenisierung Mathematik (DE-588)4403079-4 s Mathematics and its applications 422 (DE-604)BV008163334 422 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008781669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pankov, Aleksandr A. G-convergence and homogenization of nonlinear partial differential operators Mathematics and its applications Convergence opérateur Homogénéisation (équations différentielles) ram Homogénéisation opérateur elliptique Lie, Groupes de ram Opérateur elliptique non linéaire Opérateur parabolique non linéaire Opérateurs monotones ram Convergence Homogenization (Differential equations) Nonlinear partial differential operators Konvergenz (DE-588)4032326-2 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Nichtlinearer partieller Differentialoperator (DE-588)4171764-8 gnd |
| subject_GND | (DE-588)4032326-2 (DE-588)4403079-4 (DE-588)4171764-8 |
| title | G-convergence and homogenization of nonlinear partial differential operators |
| title_auth | G-convergence and homogenization of nonlinear partial differential operators |
| title_exact_search | G-convergence and homogenization of nonlinear partial differential operators |
| title_full | G-convergence and homogenization of nonlinear partial differential operators by Alexander Pankov |
| title_fullStr | G-convergence and homogenization of nonlinear partial differential operators by Alexander Pankov |
| title_full_unstemmed | G-convergence and homogenization of nonlinear partial differential operators by Alexander Pankov |
| title_short | G-convergence and homogenization of nonlinear partial differential operators |
| title_sort | g convergence and homogenization of nonlinear partial differential operators |
| topic | Convergence opérateur Homogénéisation (équations différentielles) ram Homogénéisation opérateur elliptique Lie, Groupes de ram Opérateur elliptique non linéaire Opérateur parabolique non linéaire Opérateurs monotones ram Convergence Homogenization (Differential equations) Nonlinear partial differential operators Konvergenz (DE-588)4032326-2 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Nichtlinearer partieller Differentialoperator (DE-588)4171764-8 gnd |
| topic_facet | Convergence opérateur Homogénéisation (équations différentielles) Homogénéisation opérateur elliptique Lie, Groupes de Opérateur elliptique non linéaire Opérateur parabolique non linéaire Opérateurs monotones Convergence Homogenization (Differential equations) Nonlinear partial differential operators Konvergenz Homogenisierung Mathematik Nichtlinearer partieller Differentialoperator |
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| work_keys_str_mv | AT pankovaleksandra gconvergenceandhomogenizationofnonlinearpartialdifferentialoperators |