Dynamics of evolutionary equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Applied mathematical sciences
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 670 S. graph. Darst. |
| ISBN: | 0387983473 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128466087444480 |
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| adam_text | GEORGE R. SELL YUNCHENG YOU DYNAMICS OF EVOLUTIONARY EQUATIONS WITH 19
ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII CHAPTER 1. THE EVOLUTION OF
EVOLUTIONARY EQUATIONS 1 CHAPTER 2. DYNAMICAL SYSTEMS: BASIC THEORY 11
2.1 SEMIFLOWS AND NONLINEAR SEMIGROUPS 12 2.1.1 INVARIANT SETS 15 2.1.2
LIMIT SETS 16 2.1.3 SEMIFLOWS ON FUNCTION SPACES 19 2.1.4 ORDINARY
DIFFERENTIAL EQUATIONS ON BANACH SPACES 20 2.1.5 FLOW HOMOMORPHISMS 21
2.2 COMPACT AND K-CONTRACTING SEMIFLOWS 22 2.3 ATTRACTORS AND GLOBAL
ATTRACTORS 27 2.3.1 ASYMPTOTICAL COMPACTNESS 28 2.3.2 ATTRACTORS AND
THEIR PROPERTIES 29 2.3.3 STABILITY, DISSIPATIVITY, AND ABSORBING SETS
32 2.3.4 ATTRACTORS FOR K-CONTRACTING SEMIFLOWS 34 2.3.5 EXISTENCE OF
GLOBAL ATTRACTORS 35 2.3.6 ROBUSTNESS OF ATTRACTORS 41 2.3.7 GLOBAL
ATTRACTORS: A SUMMARY 44 2.4 SKEW PRODUCT DYNAMICS AND NONAUTONOMOUS
EQUATIONS 45 2.5 SINGULAR SEMIFLOWS 48 2.6 EXERCISES 50 2.7 COMMENTARY
53 CHAPTER 3. LINEAR SEMIGROUPS 61 3.1 CO-SEMIGROUPS AND INFINITESIMAL
GENERATORS 62 3.2 AN ILLUSTRATIVE EXAMPLE 66 X CONTENTS 3.3 COMPACT AND
K-CONTRACTING C 0 -SEMIGROUPS 69 3.4 HILLE-YOSIDA AND LUMER-PHILLIPS
THEOREMS 69 3.5 DIFFERENTIABLE SEMIGROUPS , 73 3.6 ANALYTIC SEMIGROUPS
AND SECTORIAL OPERATORS 76 3.6.1 CHARACTERIZATIONS OF ANALYTIC
SEMIGROUPS 78 3.6.2 CONSTRUCTION OF ANALYTIC SEMIGROUPS 84 3.7
FRACTIONAL POWERS AND INTERPOLATION SPACES 92 3.8 ILLUSTRATIONS 103
3.8.1 HEAT EQUATION 104 3.8.2 LINEAR PARABOLIC EQUATIONS 105 3.8.3
STOKES EQUATIONS ILL 3.8.4 WAVE EQUATION 115 3.8.5 SCHRODINGER EQUATION
119 3.8.6 THE L 1 - L REGULARITY PROPERTY OF ANALYTIC SEMIGROUPS 120
3.9 PERTURBATION THEORY 126 3.10 EXERCISES 128 3.11 COMMENTARY 137
CHAPTER 4. BASIC THEORY OF EVOLUTIONARY EQUATIONS 141 4.1 PDES AS
EVOLUTIONARY EQUATIONS ._* 143 PART I: LINEAR THEORY 146 4.2 SOLUTION
CONCEPTS AND THE VARIATION OF CONSTANTS FORMULA 146 4.2.1 Q-THEORY 148
4.2.2 ANALYTIC THEORY 152 4.2.3 COMPACT THEORY AND WEAK SOLUTIONS 161
4.2.4 THE C 0 -THEORY, REVISITED 171 4.3 LINEAR SKEW PRODUCT SEMIFLOWS
172 4.4 PERTURBATIONS OF ANALYTIC SEMIGROUPS 175 4.4.1 A BASIC THEOREM
177 4.4.2 TOPOLOGICAL ISSUES 185 4.4.3 STRONG SOLUTIONS 188 4.5
EXPONENTIAL DICHOTOMIES: EXISTENCE AND ROBUSTNESS 190 4.5.1 EXPONENTIAL
DICHOTOMY 192 4.5.2 INHOMOGENEOUS EQUATIONS 203 4.5.3 DISCRETE
INHOMOGENEOUS EQUATIONS 210 4.5.4 ROBUSTNESS THEOREMS 216 PART II:
NONLINEAR THEORY 221 4.6 WELL-POSED PROBLEMS: C 0 -THEORY 224 4.6.1
LOCAL EXISTENCE AND UNIQUENESS THEOREMS 225 CONTENTS XI 4.6.2 MAXIMALLY
DEFINED SOLUTIONS 228 4.6.3 CONTINUOUS DEPENDENCE OF SOLUTIONS 229 4.6.4
CONSTRUCTION OF THE NONLINEAR SEMIFLOW 231 4.7 WELL-POSED PROBLEMS:
ANALYTIC THEORY 232 4.7.1 MILD SOLUTIONS 233 4.7.2 STRONG SOLUTIONS 234
4.7.3 MAXIMALLY DEFINED SOLUTIONS 235 4.7.4 CONTINUOUS DEPENDENCE OF
SOLUTIONS 236 4.7.5 CONSTRUCTION OF THE NONLINEAR SEMIFLOW 237 4.7.6
EXTENSION OF THE SEMIFLOW 239 4.8 REGULARITY AND COMPACTNESS PROPERTIES
244 4.8.1 COMPACTNESS PROPERTIES 244 4.8.2 REGULARITY IN SPACE AND TIME
246 4.9 THE LINEARIZED EQUATION 247 4.9.1 DIFFERENTIABILITY OF MILD
SOLUTIONS 249 4.9.2 THE LINEAR SKEW PRODUCT SEMIFLOW, REVISITED 251 4.10
EXERCISES 252 4.11 COMMENTARY 261 CHAPTER 5. NONLINEAR PARTIAL
DIFFERENTIAL EQUATIONS 267 5.1 REACTION DIFFUSION EQUATIONS 269 5.1.1
THE CHAFEE-INFANTE EQUATIONS 269 5.1.2 SYSTEMS OF EQUATIONS AND
INHOMOGENEOUS BOUNDARY CONDITIONS 281 5.1.3 PARTLY DISSIPATIVE SYSTEMS
283 5.2 NONLINEAR WAVE EQUATIONS 284 5.2.1 ABSTRACT NONLINEAR WAVE
EQUATIONS 285 5.2.2 NONLINEAR DAMPED BEAM EQUATION 293 5.2.3 NONLINEAR
WAVE EQUATIONS WITH LOCAL DAMPING 299 5.3 EQUATIONS OF CONVECTION 313
5.3.1 CONSTRUCTION OF THE SEMIFLOW 314 5.3.2 GLOBAL ATTRACTOR IN V 318
5.4 KURAMOTO-SIVASHINSKY EQUATION 319 5.4.1 THE ANITSYMMETRIC CASE 321
5.4.2 THE GENERAL CASE 327 5.5 CAHN-HILLIARD EQUATION 328 5.5.1
CONSTRUCTION OF THE SEMIFLOW 329 5.5.2 ATTRACTORS FOR THE CAHN-HILLIARD
EQUATION 335 5.6 EXERCISES 339 5.7 COMMENTARY 348 CHAPTER 6.
NAVIER-STOKES DYNAMICS 359 6.1 FORMULATION AS A NONLINEAR EVOLUTIONARY
EQUATION 361 XII CONTENTS 6.1.1 THE STOKES OPERATOR, REVISITED 362 6.1.2
THE NONLINEARITY 364 6.2 BUBNOV-GALERKIN APPROXIMATIONS 369 6.3 WEAK
SOLUTIONS R 373 6.3.1 THE LEARY-HOPF THEORY 374 6.3.2 GENERALIZED WEAK
SOLUTIONS 389 6.3.3 THE UNIQUENESS PROBLEM 395 6.4 STRONG SOLUTIONS :
396 6.4.1 TWO-DIMENSIONAL THEORY 400 6.4.2 THREE-DIMENSIONAL THEORY 401
6.4.3 THE GLOBAL REGULARITY PROBLEM 403 6.4.4 THE LINEARIZED EQUATION
406 6.4.5 HIGHER REGULARITY OF SOLUTIONS 413 6.5 NAVIER-STOKES DYNAMICS:
GLOBAL ATTRACTORS 416 6.5.1 TWO-DIMENSIONAL THEORY 416 6.5.2
THREE-DIMENSIONAL THEORY 419 6.5.3 NONAUTONOMOUS PROBLEMS 424 6.6 THE
KWAK TRANSFORMATION 426 6.7 RELATED NONLINEAR SYSTEMS 430 6.7.1
INHOMOGENEOUS BOUNDARY CONDITIONS 431 6.7.2 BENARD CONVECTION 433 6.7.3
CHEMICALLY REACTING FLOWS 434 6.8 PROOFS FOR THE BUBNOV-GALERKIN
APPROXIMATIONS 436 6.9 EXERCISES 442 6.10 COMMENTARY 450 CHAPTER 7.
MAJOR FEATURES OF DYNAMICAL SYSTEMS 457 7.1 LOCAL DYNAMICS NEAR AN
EQUILIBRIUM 460 7.1.1 UNSTABLE AND STABLE MANIFOLD THEOREMS 464 7.1.2
CENTER MANIFOLD THEOREM 473 7.1.3 PERTURBATION THEORY FOR EQUILIBRIA 481
7.2 DYNAMICS OF GRADIENT SYSTEMS 483 7.3 BEHAVIOR NEAR A PERIODIC ORBIT
488 7.4 INVARIANT MANIFOLDS 490 7.4.1 STATEMENT OF THEOREMS 496 7.4.2
LOCAL COORDINATES NEAR M 503 7.4.3 THE DYNAMICS ON M 505 7.4.4 PERTURBED
DYNAMICS NEAR M 513 7.4.5 PROOFS OF THEOREMS 540 7.5 APPLICATIONS 541
7.5.1 THE COUETTE-TAYLOR FLOW 545 7.5.2 THE BOBNOV-GALERKIN
APPROXIMATIONS 548 7.6 NONAUTONOMOUS PROBLEMS 553 7.7 OTHER TOPICS OF
DYNAMICAL SYSTEMS 553 CONTENTS XIII 7.7.1 DIFFERENTIAL DELAY EQUATIONS.
FUNCTIONAL DIFFERENTIAL EQUATIONS 553 7.7.2 BIFURCATION THEORY 553 7.7.3
ERGODIC THEORY 553 7.7.4 DIMENSION THEORY 554 7.7.5 MINIMAL SET. THE
BASIC BUILDING BLOCK 556 7.7.6 SINGULAR PERTURBATIONS 557 7.7.7
APPROXIMATION DYNAMICS 560 7.7.8 HAMILTONIAN SYSTEMS 562 7.8 EXERCISES
563 7.9 COMMENTARY 565 CHAPTER 8. INERTIAL MANIFOLDS: THE REDUCTION
PRINCIPLE 569 8.1 INTRODUCTION 570 8.2 THE LYAPUNOV-PERRON METHOD 575
8.3 EXISTENCE OF INERTIAL MANIFOLDS: SPECTRAL GAP CONDITION 577 8.4
EXPONENTIAL ATTRACTION OF INERTIAL MANIFOLDS 582 8.5 SMOOTHNESS OF
INERTIAL MANIFOLDS 585 8.6 APPLICATIONS OF INERTIAL MANIFOLD THEOREMS
589 8.7 OPEN PROBLEMS FOR INERTIAL MANIFOLDS 591 8.8 COMMENTARY 592
APPENDICES: BASICS OF FUNCTIONAL ANALYSIS 593 A BANACH SPACES AND
FRECHET SPACES 593 B FUNCTION SPACES AND SOBOLEV IMBEDDING THEOREMS 604
C CALCULUS OF VECTOR-VALUED FUNCTIONS 613 D BASIC INEQUALITIES 621 E
COMMENTARY 626 BIBLIOGRAPHY 629 NOTATION INDEX 655 SUBJECT INDEX 659
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:41Z |
| institution | BVB |
| isbn | 0387983473 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009329882 |
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| owner | DE-384 DE-355 DE-BY-UBR DE-703 DE-20 DE-29T DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188 DE-M382 DE-739 |
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| physical | XIII, 670 S. graph. Darst. |
| publishDate | 2002 |
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| series | Applied mathematical sciences |
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| spelling | Sell, George R. 1937- Verfasser (DE-588)172369576 aut Dynamics of evolutionary equations George R. Sell ; Yuncheng You New York [u.a.] Springer 2002 XIII, 670 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 143 Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Evolutionsgleichung (DE-588)4129061-6 s Partielle Differentialgleichung (DE-588)4044779-0 s You, Yuncheng Verfasser (DE-588)1056147059 aut Applied mathematical sciences 143 (DE-604)BV000005274 143 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009329882&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sell, George R. 1937- You, Yuncheng Dynamics of evolutionary equations Applied mathematical sciences Differenzierbares dynamisches System (DE-588)4137931-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4044779-0 (DE-588)4129061-6 |
| title | Dynamics of evolutionary equations |
| title_auth | Dynamics of evolutionary equations |
| title_exact_search | Dynamics of evolutionary equations |
| title_full | Dynamics of evolutionary equations George R. Sell ; Yuncheng You |
| title_fullStr | Dynamics of evolutionary equations George R. Sell ; Yuncheng You |
| title_full_unstemmed | Dynamics of evolutionary equations George R. Sell ; Yuncheng You |
| title_short | Dynamics of evolutionary equations |
| title_sort | dynamics of evolutionary equations |
| topic | Differenzierbares dynamisches System (DE-588)4137931-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Differenzierbares dynamisches System Partielle Differentialgleichung Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009329882&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
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