Nonlinear PDEs: Mathematical models in biology, chemistry and population genetics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2012
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 391 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642226632 3642226639 |
Internformat
MARC
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| 245 | 1 | 0 | |a Nonlinear PDEs |b Mathematical models in biology, chemistry and population genetics |c Marius Ghergu ; Vicenţiu D. Rădulescu |
| 264 | 1 | |a Berlin |b Springer |c 2012 | |
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Datensatz im Suchindex
| _version_ | 1805145558501818368 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 OVERVIEW OF MATHEMATICAL METHODS IN PARTIAL DIFFERENTIAL EQUATIONS 1
1.1 COMPARISON PRINCIPLES 1
1.2 RADIAL SYMMETRY OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS 6
1.3 VARIATIONAL METHODS 9
1.3.1 EKELAND'S VARIATIONAL PRINCIPLE 9
1.3.2 MOUNTAIN PASS THEOREM 11
1.3.3 AROUND THE PALAIS-SMALE CONDITION
FOR EVEN FUNCTIONALS 12
1.3.4 BOLLE'S VARIATIONAL METHOD FOR BROKEN SYMMETRIES 14
1.4 DEGREE THEORY 15
1.4.1 BROUWER DEGREE 15
1.4.2 LERAY-SCHAUDER DEGREE 16
1.4.3 LERAY-SCHAUDER DEGREE FOR ISOLATED SOLUTIONS 17
2 LIOUVILLE TYPE THEOREMS FOR ELLIPTIC OPERATORS
IN DIVERGENCE FORM 19
2.1 INTRODUCTION 19
2.2 SOME RELATED ODE PROBLEMS 21
2.3 MAIN RESULTS 26
3 BLOW-UP BOUNDARY SOLUTIONS OF THE LOGISTIC EQUATION 29
3.1 SINGULAR SOLUTIONS OF THE LOGISTIC EQUATION 30
3.1.1 A KARAMATA REGULAR VARIATION THEORY APPROACH 43
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1012996425
DIGITALISIERT DURCH
IMAGE 2
X VJ CONTENTS
3.2 KELLER-OSSERMAN CONDITION REVISITED 60
3.2.1 SETTING OF THE PROBLEM 61
3.2.2 MINIMALITY PRINCIPLE 65
3.2.3 EXISTENCE OF SOLUTIONS ON SOME BALL 70
3.2.4 EXISTENCE OF SOLUTIONS ON SMALL BALLS 72
3.2.5 EXISTENCE OF SOLUTIONS ON SMOOTH DOMAINS 73
3.2.6 BLOW-UP RATE OF RADIALLY SYMMETRIC SOLUTIONS 74
3.2.7 BLOW-UP RATE OF SOLUTIONS ON SMOOTH DOMAINS 75
3.2.8 A UNIQUENESS RESULT 77
3.2.9 DISCRETE EQUATIONS 79
3.2.10 NUMERICAL COMPUTATIONS 86
3.3 ENTIRE LARGE SOLUTIONS 91
3.3.1 A USEFUL RESULT: BOUNDED ENTIRE SOLUTIONS 91
3.3.2 EXISTENCE OF AN ENTIRE LARGE SOLUTION 93
3.3.3 UNIQUENESS OF SOLUTION 98
3.4 ELLIPTIC EQUATIONS WITH ABSORPTION 100
3.5 LACK OF THE KELLER-OSSERMAN CONDITION 106
4 SINGULAR LANE-EMDEN-FOWLER EQUATIONS AND SYSTEMS 117
4.1 BIFURCATION PROBLEMS FOR SINGULAR ELLIPTIC EQUATIONS 117
4.2 LANE-EMDEN-FOWLER SYSTEMS WITH NEGATIVE EXPONENTS 130
4.2.1 PRELIMINARY RESULTS 132
4.2.2 NONEXISTENCE OF A SOLUTION 139
4.2.3 EXISTENCE OF A SOLUTION 142
4.2.4 REGULARITY OF SOLUTION 149
4.2.5 UNIQUENESS 153
4.3 SUBLINEAR LANE-EMDEN SYSTEMS WITH SINGULAR DATA 155
4.3.1 CASE P 0 AND Q 0 155
4.3.2 CASE P 0 AND Q 0 158
4.3.3 CASE P 0 AND Q 0 162
4.3.4 FURTHER EXTENSIONS: SUPERLINEAR CASE 163
5 SINGULAR ELLIPTIC INEQUALITIES IN EXTERIOR DOMAINS 167
5.1 INTRODUCTION 167
5.2 SOME ELLIPTIC PROBLEMS IN BOUNDED DOMAINS 168
IMAGE 3
CONTENTS XVII
5.3 AN EQUIVALENT INTEGRAL CONDITION 174
5.4 THE NONDEGENERATE CASE 175
5.4.1 NONEXISTENCE RESULTS 175
5.4.2 EXISTENCE RESULTS 180
5.5 THE DEGENERATE CASE 188
5.6 APPLICATION TO SINGULAR ELLIPTIC SYSTEMS IN EXTERIOR DOMAINS 203
6 TWO QUASILINEAR ELLIPTIC PROBLEMS 211
6.1 A DEGENERATE ELLIPTIC PROBLEM WITH LACK OF COMPACTNESS 211
6.1.1 INTRODUCTION 211
6.1.2 AUXILIARY RESULTS 214
6.1.3 PROOF OF THE MAIN RESULT 222
6.2 A QUASILINEAR ELLIPTIC PROBLEM FOR P-LAPLACE OPERATOR 227
7 SOME CLASSES OF POLYHARMONIC PROBLEMS 245
7.1 AN EIGENVALUE PROBLEM WITH CONTINUOUS SPECTRUM 245
7.2 INFINITELY MANY SOLUTIONS FOR PERTURBED NONLINEARITIES 251
7.3 A BIHARMONIC PROBLEM WITH SINGULAR NONLINEARITY 258
8 LARGE TIME BEHAVIOR OF SOLUTIONS FOR DEGENERATE PARABOLIC
EQUATIONS 267
8.1 INTRODUCTION 267
8.2 SUPERLINEAR CASE 268
8.3 SUBLINEAR CASE 275
8.4 LINEAR CASE 283
9 REACTION-DIFFUSION SYSTEMS ARISING IN CHEMISTRY 287
9.1 INTRODUCTION 287
9.2 BRUSSELATOR MODEL 288
9.2.1 EXISTENCE OF GLOBAL SOLUTIONS 290
9.2.2 STABILITY OF THE UNIFORM STEADY STATE 293
9.2.3 DIFFUSION-DRIVEN INSTABILITY 295
9.2.4 A PRIORI ESTIMATES 296
9.2.5 NONEXISTENCE RESULTS 299
9.2.6 EXISTENCE RESULTS 302
IMAGE 4
X V I II CONTENTS
9.3 SCHNACKENBERG MODEL 306
9.3.1 THE EVOLUTION SYSTEM AND GLOBAL SOLUTIONS 307
9.3.2 A PRIORI ESTIMATES 310
9.3.3 NONEXISTENCE OF NONCONSTANT STEADY STATES 314
9.3.4 EXISTENCE RESULTS 317
9.4 LENGYEL-EPSTEIN MODEL 322
9.4.1 GLOBAL SOLUTIONS IN TIME 323
9.4.2 TURING INSTABILITIES 326
9.4.3 A PRIORI ESTIMATES FOR STATIONARY SOLUTIONS 328
9.4.4 NONEXISTENCE RESULTS 330
9.4.5 EXISTENCE 332
10 PATTERN FORMATION AND THE GIERER-MEINHARDT MODEL
IN MOLECULAR BIOLOGY 337
10.1 INTRODUCTION 337
10.2 SOME PRELIMINARIES 340
10.3 CASE 0 P 1 347
10.3.1 EXISTENCE 347
10.3.2 FURTHER RESULTS ON REGULARITY 354
10.3.3 UNIQUENESS OF A SOLUTION 356
10.4 CASE P 0 362
10.4.1 A NONEXISTENCE RESULT 362
10.4.2 EXISTENCE 364
A CAFFARELLI-KOHN-NIRENBERG INEQUALITY 369
B ESTIMATES FOR THE GREEN FUNCTION ASSOCIATED
TO THE BIHARMONIC OPERATOR 373
REFERENCES 377
INDEX 337 |
| any_adam_object | 1 |
| author | Ghergu, Marius Rădulescu, Vicenţiu D. 1958- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783642226632 3642226639 |
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| spelling | Ghergu, Marius Verfasser aut Nonlinear PDEs Mathematical models in biology, chemistry and population genetics Marius Ghergu ; Vicenţiu D. Rădulescu Berlin Springer 2012 XVIII, 391 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Monographs in Mathematics Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s DE-604 Rădulescu, Vicenţiu D. 1958- Verfasser (DE-588)138708924 aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3845100&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024551399&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghergu, Marius Rădulescu, Vicenţiu D. 1958- Nonlinear PDEs Mathematical models in biology, chemistry and population genetics Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4128900-6 |
| title | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics |
| title_auth | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics |
| title_exact_search | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics |
| title_full | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics Marius Ghergu ; Vicenţiu D. Rădulescu |
| title_fullStr | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics Marius Ghergu ; Vicenţiu D. Rădulescu |
| title_full_unstemmed | Nonlinear PDEs Mathematical models in biology, chemistry and population genetics Marius Ghergu ; Vicenţiu D. Rădulescu |
| title_short | Nonlinear PDEs |
| title_sort | nonlinear pdes mathematical models in biology chemistry and population genetics |
| title_sub | Mathematical models in biology, chemistry and population genetics |
| topic | Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Nichtlineare partielle Differentialgleichung |
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