Matched asymptotic expansions in reaction diffusion theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; Berlin ; Heidelberg ; New York ; Hong Kong ; Milan ; Pa
Springer
2004
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 283 - 287 |
| Physical Description: | X, 290 S. graph. Darst. : 24 cm |
| ISBN: | 1852337672 |
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MARC
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| 100 | 1 | |a Leach, John A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matched asymptotic expansions in reaction diffusion theory |c J. A. Leach ; D. J. Needham |
| 264 | 1 | |a London ; Berlin ; Heidelberg ; New York ; Hong Kong ; Milan ; Pa |b Springer |c 2004 | |
| 300 | |a X, 290 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Literaturverz. S. 283 - 287 | ||
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Reaction-diffusion equations | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Needham, David J. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | J.A. LEACH D.J. NEEDHAM MATCHED ASYMPTOTIC EXPANSIONS IN
REACTION-DIFFUSION THEORY WITH 52 FIGURES SPRINGER CONTENTS PART I THE
EVOLUTION OF TRAVELLING WAVES IN SCALAR FISHER- KOLMOGOROV EQUATIONS 1
INTRODUCTION 3 1.1 GENERALIZED FISHER NONLINEARITY 5 1.2 MTH-ORDER (M
1) FISHER NONLINEARITY 10 2 GENERALIZED FISHER NONLINEARITY 15 2.1
PERMANENT FORM TRAVELLING WAVES 15 2.2 ASYMPTOTIC SOLUTION TO IBVP AS T
- * OO 17 2.2.1 CASE (III): V* 2 18 2.2.2 CASE (II): V* = 2, U T {Z,
V*) ~ B*E~ Z AS Z - OO 31 2.2.3 CASE (I): U* = 2, U T (Z,I;*) ~ A*ZE-*
AS Z - * OO 33 2.2.4 CONCLUSIONS 34 2.3 EXAMPLE: FISHER S GENERAL
GENETIC POPULATION MODEL 35 3 RATH-ORDER (RA 1) FISHER NONLINEARITY:
INITIAL DATA WITH EXPONENTIAL DECAY RATES OR COMPACT SUPPORT 39 3.1
PERMANENT FORM TRAVELLING WAVES 40 3.2 EVOLUTION OF TRAVELLING WAVES IN
[P, M] 41 3.2.1 ASYMPTOTIC SOLUTION AS T - 0 FOR 0 X OO 41 3.2.2
ASYMPTOTIC SOLUTION AS X - OO FOR T = 0(1) 43 3.2.3 ASYMPTOTIC SOLUTION
AS T - OO IN THE CASE OF INITIAL DATA WITH EXPONENTIAL DECAY RATE AS X
-» OO 43 3.2.4 ASYMPTOTIC SOLUTION AS T *I OO IN THE CASE OF INITIAL
DATA WITH COMPACT SUPPORT 60 3.3 NUMERICAL SOLUTIONS 66 3.3.1 NUMERICAL
SOLUTIONS WHEN THE INITIAL DATA HAS EXPONENTIAL DECAY RATE AS X * OO 67
3.3.2 NUMERICAL SOLUTIONS WHEN THE INITIAL DATA HAS COMPACT SUPPORT 69
VIII CONTENTS 3.4 SUMMARY 69 3.4.1 INITIAL DATA WITH EXPONENTIAL DECAY
AS X * OO 69 3.4.2 INITIAL DATA WITH COMPACT SUPPORT 71 3.5
CONSIDERATION OF A MORE GENERAL CLASS OF INITIAL DATA WITH EXPONENTIAL
DECAY RATE AS X - * OO 72 4 RATH-ORDER (RA 1) FISHER NONLINEARITY:
INITIAL DATA WITH ALGEBRAIC DECAY RATES 75 4.1 PERMANENT FORM TRAVELLING
WAVES 75 4.2 ASYMPTOTIC SOLUTION AS T - * 0 FOR 0 X OO 76 4.3
ASYMPTOTIC SOLUTION AS X -» OO FOR T * O(L) 77 4-3- 1 =^T 77 4 -3-2
^ I 78 4.4 ASYMPTOTIC SOLUTION AS T - OO WHEN A = ^-J- 79 4.4.1 KM 2 79
4.4.2 M = 2 88 4.4.3 M 2 91 4.5 ASYMPTOTIC SOLUTION AS T * OO WHEN A
-^ZI 96 4.6 NUMERICAL SOLUTIONS 99 4.7 SUMMARY 106 5 EXTENSION TO
SYSTEMS OF FISHER-KOLMOGOROV EQUATIONS. EXAMPLE: A SIMPLE MODEL FOR AN
IONIC AUTOCATALYTIC SYSTEM ILL 5.1 GENERAL PROPERTIES OF TRAVELLING WAVE
SOLUTIONS 114 5.1.1 SUMMARY 119 5.2 THE EXISTENCE OF TRAVELLING WAVE
SOLUTIONS 119 5.2.1 EQUIVALENT DYNAMICAL SYSTEM 120 5.3 THE INITIAL
VALUE PROBLEM (IVP) 122 5.4 ASYMPTOTIC SOLUTION TO IVP AS T - OO 124
5.4.1 ASYMPTOTIC SOLUTION AS T -+ 0 125 5.4.2 ASYMPTOTIC SOLUTION AS
|A;| * OO 129 5.4.3 ASYMPTOTIC SOLUTION AS T * OO 130 5.4.4 SUMMARY
142 5.5 NUMERICAL SOLUTIONS 144 5.6 CONCLUSIONS 146 PART II THE ANALYSIS
OF A CLASS OF SINGULAR SCALAR REACTION- DIFFUSION EQUATIONS 6
INTRODUCTION 151 CONTENTS IX PERMANENT FORM TRAVELLING WAVES (PTWS) 155
7.1 GENERAL PROPERTIES OF PTW SOLUTIONS 155 7.2 PTW SOLUTIONS WHEN M N
157 7.2.1 LOCAL BEHAVIOUR 159 7.2.2 EXISTENCE OF A PTW CONNECTION 164
7.2.3 PROPERTIES OF THE PTW CONNECTION 167 7.3 NONEXISTENCE OF PTW
SOLUTIONS WHEN N M 168 7.4 NONEXISTENCE OF PTW SOLUTIONS WHEN N = M
171 7.5 ASYMPTOTIC FORMS FOR C*(K) 171 7.5.1 K - 0+ 171 7.5.2 K - K~
173 7.6 CONCLUSIONS AND FURTHER DISCUSSION 174 7.6.1 EXTENSION OF THE
RESULTS ON NONEXISTENCE OF PTW SOLUTIONS TO A WIDER CLASS OF SINGULAR
REACTION-DIFFUSION PROBLEMS 175 THE INITIAL-BOUNDARY VALUE PROBLEM 177
8.1 EXISTENCE, UNIQUENESS, AND THE COMPARISON THEOREM 178 8.1.1
COMPARISON THEOREM 178 8.1.2 EXISTENCE AND UNIQUENESS FOR IBVP 178 8.2
QUALITATIVE BEHAVIOUR OF THE SOLUTION TO IBVP FOR M N .... 179 8.3
QUALITATIVE BEHAVIOUR OF THE SOLUTION TO IBVP FOR M * N 179 8.3.1 K 1
179 8.3.2 K = 1 181 8.3.3 K 1 182 8.4 QUALITATIVE BEHAVIOUR OF THE
SOLUTION TO IBVP FOR M N 182 8.4.1 K K* 183 8.4.2 K C 184 8.4.3 K =
K C 187 8.4.4 0 K K C 188 8.5 ASYMPTOTIC SOLUTION AS T * 0 FOR 0
A; OO 191 8.5.1 M 191 8.5.2 M = N 191 8.5.3 M N 201 8.5.4 SUMMARY
201 8.6 ASYMPTOTIC SOLUTION AS T -» OO OR AS T - T~ 201 8.6.1 M 201
8.6.2 M = N 202 8.6.3 M N 206 8.7 CONCLUSIONS 209 ASYMPTOTIC SOLUTION
OF IBVP AS T * * 0 FOR 0 X OO: INITIAL DATA WITH EXPONENTIAL OR
ALGEBRAIC DECAY RATES ... 213 9.1 INITIAL DATA WITH ALGEBRAIC DECAY AS X
- OO 213 9.2 INITIAL DATA WITH EXPONENTIAL DECAY AS X - OO 216 X
CONTENTS 9.3 SUMMARY AND FURTHER DISCUSSION 219 10 EXTENSION TO THE
SYSTEM OF SINGULAR REACTION-DIFFUSION EQUATIONS 221 10.1 THE
WELL-STIRRED CASE 223 10.1.1 THE PHASE PORTRAIT 223 10.1.2 IVPI 226
10.1.3 IVP 2 228 10.1.4 SUMMARY 229 10.2 ASYMPTOTIC SOLUTION AS T - * 0
230 10.2.1 M 230 10.2.2 M = N 241 10.2.3 M N 267 10.3 CONCLUSIONS 268
A CONSTRUCTION OF A GLOBAL NONNEGATIVE SOLUTION TO THE SCALAR EQUATION
WT = W XX + FI*W N 271 B ASYMPTOTIC SOLUTIONS TO THE EIGENVALUE PROBLEM
(8.68)-(8.71) AS RA - * 0+ AND RA - * 1~ 273 C ANALYSIS OF BOUNDARY
VALUE PROBLEM (8.76)-(8.78) 277 D ANALYSIS OF BOUNDARY VALUE PROBLEM
(8.90)-(8.92) 281 REFERENCES 283 INDEX 289
|
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| id | DE-604.BV017492089 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:18:41Z |
| institution | BVB |
| isbn | 1852337672 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010537754 |
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| physical | X, 290 S. graph. Darst. : 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Leach, John A. Verfasser aut Matched asymptotic expansions in reaction diffusion theory J. A. Leach ; D. J. Needham London ; Berlin ; Heidelberg ; New York ; Hong Kong ; Milan ; Pa Springer 2004 X, 290 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 283 - 287 Asymptotic expansions Reaction-diffusion equations Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Needham, David J. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537754&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leach, John A. Needham, David J. Matched asymptotic expansions in reaction diffusion theory Asymptotic expansions Reaction-diffusion equations Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| subject_GND | (DE-588)4323967-5 (DE-588)4112609-9 |
| title | Matched asymptotic expansions in reaction diffusion theory |
| title_auth | Matched asymptotic expansions in reaction diffusion theory |
| title_exact_search | Matched asymptotic expansions in reaction diffusion theory |
| title_full | Matched asymptotic expansions in reaction diffusion theory J. A. Leach ; D. J. Needham |
| title_fullStr | Matched asymptotic expansions in reaction diffusion theory J. A. Leach ; D. J. Needham |
| title_full_unstemmed | Matched asymptotic expansions in reaction diffusion theory J. A. Leach ; D. J. Needham |
| title_short | Matched asymptotic expansions in reaction diffusion theory |
| title_sort | matched asymptotic expansions in reaction diffusion theory |
| topic | Asymptotic expansions Reaction-diffusion equations Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| topic_facet | Asymptotic expansions Reaction-diffusion equations Reaktions-Diffusionsgleichung Asymptotische Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537754&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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