A stability index analysis of 1-D patterns of the Gray-Scott model:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2002
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| Series: | Memoirs of the American Mathematical Society
737 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 155, number 737 (third of 5 numbers)." |
| Physical Description: | XI, 64 S. graph. Darst. |
| ISBN: | 0821827391 |
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| adam_text | OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 737 A STABILITY INDEX
ANALYSIS OF 1-D PATTERNS OF THE GRAY-SCOTT MODEL ARJEN DOELMAN ROBERT A.
GARDNER TASSO J. KAPER JANUARY 2002 * VOLUME 155 * NUMBER 737 (THIRD OF
5 NUMBERS) * ISSN 0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE,
RHODE ISLAND CONTENTS PREFACE XI CHAPTER 1. INTRODUCTION 1 1.1. THE
GRAY-SCOTT MODEL: BACKGROUND 1 1.2. ASYINPTOTIC ANALYSIS OF THE WAVE 4
1.3. THE NONLOCAL EIGENVALUE PROBLEM (NLEP) 5 1.4. THE MAIN RESULTS 11
CHAPTER 2. THE EVANS FUNCTION AND THE STABILITY INDEX 13 2.1. THE
LINEARIZED EQUATIONS 13 2.2. THE EVANS FUNCTION 14 2.3. THE STABILITY
INDEX 19 2.4. OUTLINE AND ENDGAME OF THE PROOF 23 CHAPTER 3. TRACKING
THE FAST SUBBUNDLE * 25 3.1. ASYMPTOTIC AND REDUCED EQUATIONS IN THE
FAST SCALING 26 3.2. A LARGE A ESTIMATE 27 3.3. INVARIANT SETS FOR THE
PROJECTIVIZED FLOW 29 3.4. COROLLARIES OF THE FAST TRACKING THEOREM 32
CHAPTER 4. THE SLOW SUBBUNDLE 37 4.1. DEFINITION OF THE SLOW SOLUTION 37
4.2. TRACKING THE SLOW SOLUTION OVER THE SLOW FIELDS 38 4.3. TRACKING
THE SLOW SOLUTION OVER THE FAST FIELD 44 4.4. THE CONSTRUCTION OF S
{K,S) 54 CHAPTER 5. CALCULATION OF THE STABILITY INDEX 57 5.1. THE
STRONGLY UNSTABLE REGIME: 0 0 1/2 58 5.2. THE OTHER REGIMES: 1/2 0
1 58 CHAPTER 6. CONCLUDING REMARKS 61 BIBLIOGRAPHY 63
|
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| author | Doelman, Arjen Gardner, Robert A. Kaper, Tasso J. 1964- |
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| id | DE-604.BV014196925 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:24Z |
| institution | BVB |
| isbn | 0821827391 |
| language | English |
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| oclc_num | 47825738 |
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| physical | XI, 64 S. graph. Darst. |
| publishDate | 2002 |
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| series | Memoirs of the American Mathematical Society |
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| spelling | Doelman, Arjen Verfasser (DE-588)1294378279 aut A stability index analysis of 1-D patterns of the Gray-Scott model Arjen Doelman ; Robert A. Gardner ; Tasso J. Kaper Providence, RI AMS 2002 XI, 64 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 737 "Volume 155, number 737 (third of 5 numbers)." Partiële differentiaalvergelijkingen gtt Eigenvalues Perturbation (Mathematics) Reaction-diffusion equations Störungstheorie (DE-588)4128420-3 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Störungstheorie (DE-588)4128420-3 s Eigenwert (DE-588)4151200-5 s DE-604 Gardner, Robert A. Verfasser (DE-588)1294378848 aut Kaper, Tasso J. 1964- Verfasser (DE-588)173521010 aut Memoirs of the American Mathematical Society 737 (DE-604)BV008000141 737 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009731703&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doelman, Arjen Gardner, Robert A. Kaper, Tasso J. 1964- A stability index analysis of 1-D patterns of the Gray-Scott model Memoirs of the American Mathematical Society Partiële differentiaalvergelijkingen gtt Eigenvalues Perturbation (Mathematics) Reaction-diffusion equations Störungstheorie (DE-588)4128420-3 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Eigenwert (DE-588)4151200-5 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4323967-5 (DE-588)4151200-5 |
| title | A stability index analysis of 1-D patterns of the Gray-Scott model |
| title_auth | A stability index analysis of 1-D patterns of the Gray-Scott model |
| title_exact_search | A stability index analysis of 1-D patterns of the Gray-Scott model |
| title_full | A stability index analysis of 1-D patterns of the Gray-Scott model Arjen Doelman ; Robert A. Gardner ; Tasso J. Kaper |
| title_fullStr | A stability index analysis of 1-D patterns of the Gray-Scott model Arjen Doelman ; Robert A. Gardner ; Tasso J. Kaper |
| title_full_unstemmed | A stability index analysis of 1-D patterns of the Gray-Scott model Arjen Doelman ; Robert A. Gardner ; Tasso J. Kaper |
| title_short | A stability index analysis of 1-D patterns of the Gray-Scott model |
| title_sort | a stability index analysis of 1 d patterns of the gray scott model |
| topic | Partiële differentiaalvergelijkingen gtt Eigenvalues Perturbation (Mathematics) Reaction-diffusion equations Störungstheorie (DE-588)4128420-3 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Eigenwert (DE-588)4151200-5 gnd |
| topic_facet | Partiële differentiaalvergelijkingen Eigenvalues Perturbation (Mathematics) Reaction-diffusion equations Störungstheorie Reaktions-Diffusionsgleichung Eigenwert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009731703&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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