Asymptotic analysis of singular perturbations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1979
|
| Series: | Studies in mathematics and its applications
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 286 S. |
| ISBN: | 0444853065 |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
ASYMPTOTIC ANALYSIS OF
SINGULAR PERTURBATIONS
WIKTOR ECKHAUS MATHEMATISCH INSTITUUT RIJKSUNIVERSITEIT UTRECHT
SUE C
M 1979
NORTH-HOLLAND PUBLISHING COMPANY AMSTERDAM * NEW YORK * OXFORD
IMAGE 2
CONTENTS
PREFACE VII
CONTENTS IX
CHAPTER 1. ASYMPTOTIC DEFINITIONS AND PROPERTIES 1
1.1. ORDER SYMBOLS, SHARP ESTIMATES AND ORDER FUNCTIONS 1
1.2. ASYMPTOTIC SEQUENCES AND ASYMPTOTIC SERIES 5
1.3. ORDERS OF MAGNITUDE 8
1.4. ASYMPTOTIC APPROXIMATIONS AND ASYMPTOTIC EXPANSIONS 11
1.5. REGULAER APPROXIMATIONS AND REGULAER EXPANSIONS 16
1.6. GAUGE FUNCTIONS, GAUGE SETS AND THE UNIQUENESS OF REGULAER
EXPANSIONS 19
CHAPTER 2. FUNCTIONS WITH SINGULARITIES ON SUBSETS OF LOWER DIMENSION
(BOUNDARY LAYERS) , 21
2.1. QUALITATIVE DESCRIPTION OF SINGULAR BEHAVIOUR 22
2.2. REGULARITY IN SUBDOMAINS. EXTENSION THEOREMS 23
2.3. LOCAL ANALYSIS OF CONTINUOUS FUNCTIONS; LOCAL LIMIT FUNCTIONS AND
LOCAL EXPANSIONS 29
2.4. THE FORMALISM OF EXPANSION OPERATORS 33
CHAPTER 3. MATCHING RELATIONS AND COMPOSITE EXPANSIONS 38
3.1. SIGNIFICANT APPROXIMATIONS AND BOUNDARY LAYER VARIABLES 40
3.2. FURTHER APPLICATIONS OF THE EXTENSION THEOREMS; THE OVERLAP
HYPOTHESIS 42
3.3. MATCHING IN THE INTERMEDIATE VARIABLES AND UNIFORM APPROXIMATIONS
ON THE BASIS OF THE OVERLAP HYPOTHESIS 50
3.4. OVERLAP HYPOTHESIS AND INTERMEDIATE MATCHING IN THE CASE MORE
GENERAL LOCAL EXPANSIONS 53
IMAGE 3
CONTENTS
3.5. CORRECTION LAYERS AND COMPOSITE EXPANSIONS; AN ASYMPTOTIC MATCHING
PRINCIPLE 55
3.6. COMPOSITE EXPANSIONS AND AN ASYMPTOTIC MATCHING PRINCIPLE FROM
THE.HYPOTHESIS OF REGULARIZING LAYER 59
3.7. ASYMPTOTIC MATCHING PRINCIPLES AND COMPOSITE EXPANSIONS FROM THE
OVERLAP HYPOTHESIS 61
3.8. VALIDITY OF ASYMPTOTIC MATCHING PRINCIPLE WITHOUT OVERLAP 66
APPENDIX: PROOFOF THEOREM 3.7.1. 68
CHAPTER 4. HEURISTIC ANALYSIS OF SINGULAR PERTURBATIONS. LINEAR PROBLEMS
76
4.1. DEGENERATIONS OF LINEAR DIFFERENTIAL OPERATORS 77
4.2. THE DIFFERENTIAL EQUATIONS FOR THE FIRST TERM OF THE REGULAER AND
THE LOCAL EXPANSIONS 87
4.3. RECURRENCE RELATIONS FOR REGULAER AND LOCAL EXPANSIONS 91
4.4. THE CORRESPONDENCE PRINCIPLE 98
4.5. FURTHER DEVELOPMENT OF THE HEURISTIC ANALYSIS: SOME ONEDIMENSIONAL
PROBLEMS 102
4.6. HEURISTIC ANALYSIS CONTINUED: SOME TWO-DIMENSIONAL PROBLEMS 116
4.7. THE CONCEPT OF FORMAL APPROXIMATIONS 120
4.8. EXPANSIONS WITH A REGULARIZING FACTOR: THE WKB APPROXIMATION 133
4.9. EXPANSION BY THE METHOD OF MULTIPLE SCALES 139
CHAPTER 5. HEURISTIC ANALYSIS CONTINUED. NON-LINEAR PROBLEMS 145
5.1. DEGENERATIONS OF NON-LINEAR OPERATORS 146
5.2. THE DIFFERENTIAL EQUATIONS FOR THE FIRST TERMS OF THE REGULAER AND
THE LOCAL EXPANSIONS 148
5.3. THE DIFFERENTIAL EQUATIONS FOR THE HIGHER ORDER TERMS OF THE
EXPANSIONS 150
5.4. ANALYSIS OF SOME ONE-DIMENSIONAL PROBLEMS 153
5.5. SIGNIFICANT DEGENERATIONS AND THE CORRESPONDENCE PRINCIPLE
RECONSIDERED 163
5.6. SOME ONE-DIMENSIONAL PROBLEMS EXHIBITING STRONG NON-LINEAR EFFECTS
165 5.7. SOME ELLIPTIC SECOND ORDER PROBLEMS IN R 2 181
5.8. REMARKS ON THE FORMAL APPROXIMATIONS IN NON-LINEAR PROBLEMS 105
CHAPTER 6. FOUNDATIONS FOR A RIGOROUS THEORY OF SINGULAR PERTURBATIONS
188
6.1. GENERAL INTRODUCTORY CONSIDERATIONS 6.1.1. CLASSICAL PERTURBATION
ANALYSIS IN A BANACH SPACE 188 189
IMAGE 4
CONTENTS XI
6.1.2. REGULAER PROBLEMS 195
6.1.3. SINGULAR PROBLEMS: A CLASSIFICATION 197
6.1.4. THE PROBLEM OF VALIDITY OF FORMAL APPROXIMATIONS 198
6.2. ESTIMATES FOR LINEAR PROBLEMS 200
6.2.1. THE MAXIMUM PRINCIPLE FOR ELLIPTIC OPERATORS AND ITS APPLICATIONS
201
6.2.2. ESTIMATES IN HUBERT SPACES FROM POSITIVITY OF THE BILINEAR FORM
206 6.2.3. ESTIMATES IN HOLDER NORMS. ELLIPTIC EQUATIONS OF HIGHER ORDER
212 6.2.4. ESTIMATES FOR INITIAL VALUE PROBLEMS 220
6.3. NON-LINEAR PROBLEMS 225
6.3.1. NON-LINEAR APPLICATIONS OF THE MAXIMUM PRINCIPLE 226
6.3.2. UPPER AND LOWER SOLUTIONS 230
6.3.3. INITIAL VALUE PROBLEMS. TICHONOV S THEOREM 234
6.3.4. ESTIMATES FOR THE REMAINDER TERM BASED ON CONTRACTION MAPPING IN
A BANACH SPACE 236
CHAPTER 7. ELLIPTIC SINGULAR PERTURBATIONS 244
7.1. LINEAR OPERATORS OF SECOND ORDER. ELEMENTARY BOUNDARY LAYERS 245
7.1.1. ZEROTH ORDER DEGENERATIONS 245
7.1.2. FIRST ORDER DEGENERATIONS. SUBDOMAINS WITH ORDINARY BOUN DARY
LAYERS 248
7.1.3. FIRST ORDER DEGENERATIONS CONTINUED. PARABOLIC BOUNDARY LAYERS
255
7.2. LINEAR OPERATORS OF SECOND ORDER CONTINUED. REFINED ANALYSIS OF
BOUNDARY LAYERS 258
7.2.1. BIRTH OF BOUNDARY LAYERS 258
7.2.2. FREE LAYERS AND OTHER NON-UNIFORMITIES 262
7.3. NON-LINEAR OPERATORS OF SECOND ORDER 264
7.3.1. ZEROTH ORDER DEGENERATIONS 264
7.3.2. FIRST ORDER DEGENERATIONS 267
7.4. LINEAR OPERATORS OF HIGHER ORDER 270
7.4.1. ELLIPTIC DEGENERATIONS 270
7.4.2. FIRST ORDER DEGENERATIONS 275
BIBLIOGRAPHY 280
SUBJECT INDEX 287
|
| any_adam_object | 1 |
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| dewey-search | 515/.35 |
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| indexdate | 2024-07-09T15:42:58Z |
| institution | BVB |
| isbn | 0444853065 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001486404 |
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| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-706 DE-83 DE-11 DE-188 |
| physical | XI, 286 S. |
| psigel | TUB-nvmb |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | North-Holland |
| record_format | marc |
| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spelling | Eckhaus, Wiktor Verfasser aut Asymptotic analysis of singular perturbations Amsterdam North-Holland 1979 XI, 286 S. txt rdacontent n rdamedia nc rdacarrier Studies in mathematics and its applications 9 Couche limite Perturbation (Mathématiques) Équations différentielles - Théorie asymptotique Boundary layer Differential equations Asymptotic theory Perturbation (Mathematics) Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 s Störungstheorie (DE-588)4128420-3 s DE-604 Differentialgleichung (DE-588)4012249-9 s Asymptotik (DE-588)4126634-1 s Asymptotische Methode (DE-588)4287476-2 s Strömungsmechanik (DE-588)4077970-1 s Studies in mathematics and its applications 9 (DE-604)BV000000646 9 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486404&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eckhaus, Wiktor Asymptotic analysis of singular perturbations Studies in mathematics and its applications Couche limite Perturbation (Mathématiques) Équations différentielles - Théorie asymptotique Boundary layer Differential equations Asymptotic theory Perturbation (Mathematics) Asymptotische Methode (DE-588)4287476-2 gnd Asymptotik (DE-588)4126634-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4126634-1 (DE-588)4012249-9 (DE-588)4077970-1 (DE-588)4077459-4 (DE-588)4128420-3 |
| title | Asymptotic analysis of singular perturbations |
| title_auth | Asymptotic analysis of singular perturbations |
| title_exact_search | Asymptotic analysis of singular perturbations |
| title_full | Asymptotic analysis of singular perturbations |
| title_fullStr | Asymptotic analysis of singular perturbations |
| title_full_unstemmed | Asymptotic analysis of singular perturbations |
| title_short | Asymptotic analysis of singular perturbations |
| title_sort | asymptotic analysis of singular perturbations |
| topic | Couche limite Perturbation (Mathématiques) Équations différentielles - Théorie asymptotique Boundary layer Differential equations Asymptotic theory Perturbation (Mathematics) Asymptotische Methode (DE-588)4287476-2 gnd Asymptotik (DE-588)4126634-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Couche limite Perturbation (Mathématiques) Équations différentielles - Théorie asymptotique Boundary layer Differential equations Asymptotic theory Perturbation (Mathematics) Asymptotische Methode Asymptotik Differentialgleichung Strömungsmechanik Singularität Mathematik Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486404&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000646 |
| work_keys_str_mv | AT eckhauswiktor asymptoticanalysisofsingularperturbations |