An introduction to homogenization:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
1999
|
| Edition: | first published |
| Series: | Oxford lecture series in mathematics and its applications
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | ix, 262 Seiten Diagramme |
| ISBN: | 0198565542 9780198565543 |
Staff View
MARC
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| 100 | 1 | |a Cioranescu, Doina |d ca. 20./21. Jh. |0 (DE-588)1089308787 |4 aut | |
| 245 | 1 | 0 | |a An introduction to homogenization |c Doina Cioranescu ; Centre National de la Recherche Scientifique ; University of Paris VI and Patrizia Donato ; Department of Mathematics ; University of Rouen |
| 250 | |a first published | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 1999 | |
| 300 | |a ix, 262 Seiten |b Diagramme | ||
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| 650 | 4 | |a Homogenization (Differential equations) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction
1
1
Weak and weak* convergences in Banach spaces
9
1.1
Linear forms on Banach spaces
................... 10
1.2
Weak convergence
.......................... 12
1.3
Weak* convergence
.......................... 16
1.4
Some properties of Lp-spaces
.................... 18
1.5
Weak convergence in Lp for
1 <
ρ
<
oo
............... 21
1.6
Weak convergence in L1
....................... 22
1.7
Weak* convergence in L°°
...................... 25
2
Rapidly oscillating periodic functions
26
2.1
Periodic functions in L1
....................... 26
2.2
Examples
............................... 28
2.3
Weak limits of rapidly oscillating periodic functions
........ 33
3
Some classes of Sobolev spaces
40
3.1
Distributions
............................. 40
3.2
The spaces W1*
........................... 43
3.3
The space
H¿
and the notion of trace
............... 48
3.4
The space
#¿er
............................ 56
3.5
Vector-valued spaces of the type Lp(a. b; X)
............ 59
4
Some variational elliptic problems
64
4.1
Bilinear forms on Banach spaces
.................. 64
4.2
The Lax-Milgram theorem
..................... 65
4.3
Setting of the variational formulation
................ 69
4.4
The Dirichlet problem
........................ 71
4.5
The Neumann problem
........................ 75
4.6
The Robin problem
.......................... 78
4.7
Periodic boundary conditions
.................... 81
5
Examples of periodic composite materials
85
5.1
Setting of the problem
........................ 85
5.2
Some physical models
........................ 89
5.3
The one-dimensional case
...................... 95
5.4
Layered materials
........................... 98
viii Contents
6 Homogenization
of elliptic equations: the convergence result
107
6.1
Auxiliary periodic problems
..................... 108
6.2
The main convergence result
.................... 112
6.3
The ellipticity of the homogenized matrix
............. 115
6.4
Other formulas for the homogenized matrix
............ 120
6.5
The one and two-dimensional cases
................. 121
7
The multiple-scale method
125
7.1
The asymptotic expansion
...................... 125
7.2
Proof of the error estimate
...................... 133
8
Tartar s method of oscillating test functions
138
8.1
Proof of the main convergence result
................ 138
8.2
Convergence of the energy
...................... 142
8.3
Correctors
............................... 146
8.4
Some comparison results
....................... 152
8.5
Case of weakly converging data
................... 157
8.6
Convergence of eigenvalues
..................... 164
9
The two-scale convergence method
173
9.1
The general setting
.......................... 173
9.2
Two-scale convergence
........................ 176
9.3
Proof of the main convergence result
................ 182
9.4
A corrector result
........................... 185
10
Homogenization in linearized elasticity
188
10.1
Existence and uniqueness
...................... 190
10.2
Auxiliary periodic problems
..................... 194
10.3
Homogenization results
....................... 197
11
Homogenization of the heat equation
203
11.1
Existence and uniqueness
...................... 204
11.2
The homogenization result
...................... 211
11.3
Convergence of the energy
...................... 214
11.4
A corrector result
........................... 216
12
Homogenization of the wave equation
221
12.1
Existence and uniqueness
...................... 222
12.2
The homogenization result
...................... 231
12.3
Convergence of the energy
...................... 234
12.4
A corrector result
........................... 238
13
General approaches to the non-periodic case
241
13.1
G-convergence and H-convergence
................. 242
13.2
Compensated compactness and correctors
............. 245
13.3
Optimal bounds
........................... 248
Contents ix
Bibliography
252
Index 258
|
| any_adam_object | 1 |
| author | Cioranescu, Doina ca. 20./21. Jh Donato, Patrizia |
| author_GND | (DE-588)1089308787 (DE-588)1156196884 |
| author_facet | Cioranescu, Doina ca. 20./21. Jh Donato, Patrizia |
| author_role | aut aut |
| author_sort | Cioranescu, Doina ca. 20./21. Jh |
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| ctrlnum | (OCoLC)41612337 (DE-599)BVBBV013102197 |
| dewey-full | 515/.35 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | first published |
| format | Book |
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| id | DE-604.BV013102197 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:39:05Z |
| institution | BVB |
| isbn | 0198565542 9780198565543 |
| language | English |
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| physical | ix, 262 Seiten Diagramme |
| publishDate | 1999 |
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| publisher | Oxford University Press |
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| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Cioranescu, Doina ca. 20./21. Jh. (DE-588)1089308787 aut An introduction to homogenization Doina Cioranescu ; Centre National de la Recherche Scientifique ; University of Paris VI and Patrizia Donato ; Department of Mathematics ; University of Rouen first published Oxford Oxford University Press 1999 ix, 262 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 17 Hier auch später erschienene, unveränderte Nachdrucke Mathematisches Modell Homogenization (Differential equations) Materials Mathematical models Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Werkstoffkunde (DE-588)4079184-1 gnd rswk-swf Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Homogenisierung Mathematik (DE-588)4403079-4 s DE-604 Werkstoffkunde (DE-588)4079184-1 s Donato, Patrizia (DE-588)1156196884 aut Oxford lecture series in mathematics and its applications 17 (DE-604)BV009910017 17 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008925279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cioranescu, Doina ca. 20./21. Jh Donato, Patrizia An introduction to homogenization Oxford lecture series in mathematics and its applications Mathematisches Modell Homogenization (Differential equations) Materials Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Werkstoffkunde (DE-588)4079184-1 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4079184-1 (DE-588)4403079-4 |
| title | An introduction to homogenization |
| title_auth | An introduction to homogenization |
| title_exact_search | An introduction to homogenization |
| title_full | An introduction to homogenization Doina Cioranescu ; Centre National de la Recherche Scientifique ; University of Paris VI and Patrizia Donato ; Department of Mathematics ; University of Rouen |
| title_fullStr | An introduction to homogenization Doina Cioranescu ; Centre National de la Recherche Scientifique ; University of Paris VI and Patrizia Donato ; Department of Mathematics ; University of Rouen |
| title_full_unstemmed | An introduction to homogenization Doina Cioranescu ; Centre National de la Recherche Scientifique ; University of Paris VI and Patrizia Donato ; Department of Mathematics ; University of Rouen |
| title_short | An introduction to homogenization |
| title_sort | an introduction to homogenization |
| topic | Mathematisches Modell Homogenization (Differential equations) Materials Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Werkstoffkunde (DE-588)4079184-1 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd |
| topic_facet | Mathematisches Modell Homogenization (Differential equations) Materials Mathematical models Differentialgleichung Werkstoffkunde Homogenisierung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008925279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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