Tangency, flow invariance for differential equations, and optimization problems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York u.a.
Dekker
1999
|
| Schriftenreihe: | Monographs and textbooks in pure and applied mathematics
219 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008692094&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 479 S. |
| ISBN: | 0824773411 |
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Datensatz im Suchindex
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| adam_text | TANGENCY, FLOW INVARIANCE FOR DIFFERENTIAL EQUATIONS, AND OPTIMIZATION
PROBLEMS DUMITRU MOTREANU UNIVERSITY OF LASI LASI, ROMANIA NICOLAE PAVEL
OHIO UNIVERSITY ATHENS, OHIO MARCEL DEKKER, INC. NEW YORK * BASEL
CONTENTS PREFACE V CHAPTER 1. TANGENT VECTORS TO CLOSED SETS 1 1.1.
TANGENCYINNORMED SPACES 1 1.2. TANGENCY IN BANACH MANIFOLDS 13 CHAPTER
2. FLOW-INVARIANT SETS 25 2.1. FLOW-INVARIANT SETS WITH RESPECT TO
DIFFERENTIAL EQUATIONS. NAGUMO-BREZIS THEOREM 25 2.2. GENERATION OF
SEMIGROUPS ON CLOSED SUBSETS 43 2.3. FLOW-INVARIANCE WITH RESPECT TO
VECTOR FIELDS ON DIFFERENTIABLE MANIFOLDS 54 2.4. APPLICATIONS 59 2.4.1.
INTEGRAL SURFACES OF THE FIRST ORDER PDE 59 2.4.2. INVARIANT
PARALLELEPIPEDS AND QUADRANTS. COMPONENT-WISE POSITIVE SOLUTIONS 64
2.4.3. THEOREMS OF BROUWER AND MIRANDA IN TERMS OF BOULIGAND-NAGUMO
FIELDS. ZEROS OF TANGENTIAL VECTOR FIELD 67 VN VIII CONTENTS CHAPTER 3.
SECOND ORDER DIFFERENTIAL -EQUATIONS AND FLOW-INVARIANCE 73 3.1.
FLOW-INVARIANT SETS WITH RESPECT TO A SECOND ORDER DIFFERENTIAL EQUATION
IN BANACH SPACES 73 3.2. EXTENSION TO BANACH MANIFOLDS 86 3.3.
APPLICATIONS TO FLIGHT MECHANICS (ORBITAL MOTIONS) 99 CHAPTER 4.
FLOW-INVARIANT SETS WITH RESPECT TO SEMILINEAR DIFFERENTIAL EQUATION Y 1
= AY + F (T, Y) 4.1 5-FIELDS ON A CLOSED SET 121 4.2. FLOW-INVARIANT
SETS WITH RESPECT TO SEMILINEAR EVOLUTION EQUATION U = AU + F(T,U) 125
4.3. SEMILINEAR EQUATIONS WITH DISSIPATIVE PERTURBATIONS 142 4.4. THE
EXTENSION OF THE MILD SOLUTIONS. GLOBAL EXISTENCE 165 4.5.
DIFFERENTIABLE SEMIGROUPS AND EVOLUTION OPERATORS ON BANACH MANIFOLDS
AND QUASI-FLOW-INVARIANT SETS 171 4.5.1. SEMIGROUPS 171 4.5.2. EVOLUTION
OPERATORS 186 4.6. APPLICATIONS OF 5-FIELDS TO PDE 193 CHAPTER 5. A
TRANSVERSALITY APPROACH TO FLOW-INVARIANCE 207 5.1. TRANSVERSALITY
THEORY. PARAMETRIC TRANSVEFSALITY THEOREM 207 5.2. APPLICATIONS OF
TRANSVERSALITY TO FLOW-INVARIANCE 219 CHAPTER 6. OPTIMIZATION AND
OPTIMAL CONTROL VIA TANGENTIAL CONES 227 6.1. EKELAND S VARIATIONAL
PRINCIPLE 227 CONTENTS IX 6.2. GEOMETRIC OPTIMIZATION 235 6.3. NONLINEAR
PROGRAMMING AND OPTIMAL CONTROL VIA TANGENTIAL CONES AND CLOSED RANGE
OPERATORS 259 CHAPTER 7. CRITICAL POINT THEORY ON FLOW-INVARIANT SETS
281 7.1. ELEMENTS OF CRITICAL POINT THEORY 281 7.2. MINIMAX PRINCIPLES
ON CLOSED SETS 294 7.3. APPLICATIONS TO THE THEORY OF GEODESIES 302 7.4.
NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS 319 APPENDIX 1. ELEMENTS OF
NONLINEAR ANALYSIS 329 1. STRICTLY (AND UNIFORMLY) CONVEX SPACES. THE
PROJECTION ON A CLOSED SET 329 2. DUALITY MAPPING AND WEAK DERIVATIVES
332 2.1. DEFINITIONS AND BASIC PROPERTIES 332 2.2. DUALITY MAPPING OF
SOME CONCRETE SPACES 343 2.3. WEAK DERIVATIVES AND DUALITY MAPPINGS.
KATO S LEMMA 348 3. DISSIPATIVE (ACCRETIVE, MONOTONE) SETS 350 3.1.
BASIC PROPERTIES OF DISSIPATIVE SETS 350 3.2. MAXIMAL DISSIPATIVE AND
M-DISSIPATIVE SETS 356 3.3. QUASI-DISSIPATIVE SETS ..360 4. MONOTONE AND
HEMICONTINUOUS OPERATORS 363 4.1. LOCAL BOUNDEDNESS 363 4.2. MAXIMAL
MONOTONE SETS 365 5. SUBGRADIENTS (SUBDIFFERENTIALS) 380 6. CYCLICALLY
MONOTONE SETS 385 7. EXAMPLES OF MAXIMAL MONOTONE OPERATORS 388 X
CONTENTS 8. SUBDIFFERENTIABILITY OF CONVEX FUNCTIONS. CONVEX
REGULARIZATIONS .....399 9. ON THE EQUATION Y G DX * AX * BX 408 10.
SOME CHARACTERIZATIONS OF CONVEX FUNCTIONS .... 413 11. THE
EXTENDIBILITY OF CONTINUOUS AND DISSIPATIVE OPERATORS ON CLOSED SETS 419
APPENDIX 2. THE APPROXIMATE DIFFERENCE SCHEME AND NONLINEAR SEMIGROUPS
423 1. APPROXIMATE DIFFERENCE SCHEMES (DS) 423 2. D5-LIMIT SOLUTIONS 430
3. GENERATION OF NONLINEAR SEMIGROUPS. THE EXPONENTIAL FORMULA OF
CRANDALL AND LIGGETT 432 4. EXISTENCE OF .DS-APPROXIMATE SOLUTIONS AND
FLOW-INVARIANCE ; ..438 4.1. KOBAYASHI S THEOREM 438 4.2.
FLOW-INVARIANCE THEOREMS VIA .DS-APPROXIMATE SOLUTIONS 445 APPENDIX 3.
BANACH MANIFOLDS AND VECTOR FIELDS 451 APPENDIX 4. GENERALIZED GRADIENTS
457 REFERENCES 461 INDEX 477
|
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:36:07Z |
| institution | BVB |
| isbn | 0824773411 |
| language | English |
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| series | Monographs and textbooks in pure and applied mathematics |
| series2 | Monographs and textbooks in pure and applied mathematics |
| spellingShingle | Motreanu, Dumitru Pavel, Nicolae Tangency, flow invariance for differential equations, and optimization problems Monographs and textbooks in pure and applied mathematics Algèbre intervalle Algèbre opérateur C*-algèbre Flots (dynamique différentiable) ram Optimisation mathématique ram Théorie ergodique Équations différentielles non linéaires ram Differential equations, Nonlinear Flows (Differentiable dynamical systems) Mathematical optimization Abgeschlossene Teilmenge (DE-588)4141053-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4141053-1 (DE-588)4012249-9 |
| title | Tangency, flow invariance for differential equations, and optimization problems |
| title_auth | Tangency, flow invariance for differential equations, and optimization problems |
| title_exact_search | Tangency, flow invariance for differential equations, and optimization problems |
| title_full | Tangency, flow invariance for differential equations, and optimization problems Dumitru Motreanu ; Nicolae Pavel |
| title_fullStr | Tangency, flow invariance for differential equations, and optimization problems Dumitru Motreanu ; Nicolae Pavel |
| title_full_unstemmed | Tangency, flow invariance for differential equations, and optimization problems Dumitru Motreanu ; Nicolae Pavel |
| title_short | Tangency, flow invariance for differential equations, and optimization problems |
| title_sort | tangency flow invariance for differential equations and optimization problems |
| topic | Algèbre intervalle Algèbre opérateur C*-algèbre Flots (dynamique différentiable) ram Optimisation mathématique ram Théorie ergodique Équations différentielles non linéaires ram Differential equations, Nonlinear Flows (Differentiable dynamical systems) Mathematical optimization Abgeschlossene Teilmenge (DE-588)4141053-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Algèbre intervalle Algèbre opérateur C*-algèbre Flots (dynamique différentiable) Optimisation mathématique Théorie ergodique Équations différentielles non linéaires Differential equations, Nonlinear Flows (Differentiable dynamical systems) Mathematical optimization Abgeschlossene Teilmenge Differentialgleichung |
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