Evolution equations and approximations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
River Edge, NJ [u.a.]
World Scientific
2002
|
| Series: | Series on advances in mathematics for applied sciences
61 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 498 S. |
| ISBN: | 9812380264 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | SERIES ON ADVANCES IN MATHEMATICS FOR APPLIED SCIENCES - VOL. 61
EVOLUTION EQUATIONS AND APPROXIMATIONS KAZUFUMI ITO NORTH CAROLINA STATE
UNIVERSITY, USA FRANZ KAPPEL UNIVERSITY OF GRAZ, AUSTRIA WORLD
SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * HONG KONG CONTENTS PREFACE
CHAPTER 1. DISSIPATIVE AND MAXIMAL MONOTONE OPERATORS 1 1.1 DUALITY
MAPPING AND DIRECTIONAL DERIVATIVES OF NORMS 1 1.2 DISSIPATIVE OPERATORS
9 1.3 PROPERTIES OF M-DISSIPATIVE OPERATORS 17 1.4 PERTURBATION RESULTS
FOR M-DISSIPATIVE OPERATORS 25 1.5 MAXIMAL MONOTONE OPERATORS 32 1.6
CONVEX FUNCTIONAL AND SUBDIFFERENTIALS 40 CHAPTER 2. LINEAR SEMIGROUPS
57 2.1 EXAMPLES AND BASIC DEFINITIONS 57 2.2 CAUCHY PROBLEMS AND MILD
SOLUTIONS 66 2.3 THE HILLE-YOSIDA THEOREM 74 2.4 THE LUMER-PHILLIPS
THEOREM 79 2.5 A SECOND ORDER EQUATION 83 CHAPTER 3. ANALYTIC SEMIGROUPS
89 3.1 DISSIPATIVE OPERATORS AND SESQUILINEAR FORMS 89 3.2 ANALYTIC
SEMIGROUPS 97 CHAPTER 4. APPROXIMATION OF CO-SEMIGROUPS 115 4.1 THE
TROTTER-KATO THEOREM 115 4.2 APPROXIMATION OF NONHOMOGENEOUS PROBLEMS
131 4.3 VARIATIONAL FORMULATIONS OF THE TROTTER-KATO THEOREM 135 4.4 AN
APPROXIMATION RESULT FOR ANALYTIC SEMIGROUPS 141 CHAPTER 5. NONLINEAR
SEMIGROUPS OF CONTRACTIONS 147 5.1 GENERATION OF NONLINEAR SEMIGROUPS
147 5.2 CAUCHY PROBLEMS WITH DISSIPATIVE OPERATORS 153 5.3 THE
INFINITESIMAL GENERATOR 163 5.4 NONLINEAR DIFFUSION 175 CHAPTER 6.
LOCALLY QUASI-DISSIPATIVE EVOLUTION EQUATIONS 181 6.1 LOCALLY
QUASI-DISSIPATIVE OPERATORS 183 6.2 ASSUMPTIONS ON THE OPERATORS A(T)
186 6.3 DS-APPROXIMATIONS AND FUNDAMENTAL ESTIMATES 188 XII CONTENTS 6.4
EXISTENCE OF DS-APPROXIMATIONS 202 6.5 EXISTENCE AND UNIQUENESS OF MILD
SOLUTIONS 208 6.6 AUTONOMOUS PROBLEMS 229 6.7 NONHOMOGENEOUS PROBLEMS
231 6.8 STRONG SOLUTIONS 238 6.9 QUASI-LINEAR EQUATIONS 246 6.10 A
PARABOLIC PROBLEM 253 CHAPTER 7. THE CRANDALL-PAZY CLASS 263 7.1 THE
CONDITIONS 263 7.2 EXISTENCE OF AN EVOLUTION OPERATOR 267 CHAPTER 8.
VARIATIONAL FORMULATIONS AND GELFAND TRIPLES 285 8.1 CAUCHY PROBLEMS AND
GELFAND TRIPLES 285 8.2 AN APPROXIMATION RESULT 301 CHAPTER 9.
APPLICATIONS TO CONCRETE SYSTEMS 305 9.1 DELAY-DIFFERENTIAL EQUATIONS
305 9.1.1 EQUATIONS OF RETARDED TYPE IN THE STATE SPACE C 306 9.1.2
STATE DEPENDENT DELAYS 313 9.1.3 EQUATIONS OF NEUTRAL TYPE 319 9.2
SCALAR CONSERVATION LAWS 326 9.2.1 BASIC ASSUMPTIONS AND PRELIMINARIES
326 9.2.2 GLOBALLY BOUNDED FUNCTIONS 331 9.2.3 VANISHING VISCOSITY,
QUASI-DISSIPATIVITY 333 9.2.4 /^-CONSIDERATIONS 338 9.2.5 L 1 - AND L
-ESTIMATES 342 9.2.6 W M -ESTIMATES 347 9.2.7 UNIFORMITY WITH RESPECT TO
V 354 9.2.8 THE LIMIT V . 0 361 9.2.9 THE LIMITING OPERATOR 378 9.2.10
THE GENERAL CASE 385 9.3 THE NAVIER-STOKES EQUATIONS 386 9.3.1 THE
TWO-DIMENSIONAL CASE 398 9.3.2 THE THREE-DIMENSIONAL CASE 403 CHAPTER
10. APPROXIMATION OF SOLUTIONS FOR EVOLUTION EQUATIONS 409 10.1
APPROXIMATION BY APPROXIMATING EVOLUTION PROBLEMS 409 10.2 CHERNOFF S
THEOREM 427 10.3 OPERATOR SPLITTING 440 CHAPTER 11. SEMILINEAR EVOLUTION
EQUATIONS 447 11.1 WELL-POSEDNESS ; . 447 CONTENTS XIII 11.2 DELAY
EQUATIONS WITH TIME AND STATE DEPENDENT DELAYS 458 11.3 APPROXIMATION
THEORY 463 11.4 A CONCRETE APPROXIMATION SCHEME FOR DELAY SYSTEMS 469
APPENDIX 479 A.I SOME INEQUALITIES 479 A.2 CONVERGENCE OF STEKLOV MEANS
483 A.3 SOME TECHNICAL RESULTS NEEDED IN SECTION 9.2 484 BIBLIOGRAPHY
489 LIST OF SYMBOLS 493 INDEX 495
|
| any_adam_object | 1 |
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| classification_rvk | SK 540 SK 910 |
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| dewey-full | 515/.353 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014527282 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:03:15Z |
| institution | BVB |
| isbn | 9812380264 |
| language | English |
| lccn | 2002072092 |
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| oclc_num | 49936144 |
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| owner | DE-824 DE-703 DE-11 DE-188 |
| owner_facet | DE-824 DE-703 DE-11 DE-188 |
| physical | XIII, 498 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on advances in mathematics for applied sciences |
| series2 | Series on advances in mathematics for applied sciences |
| spelling | Ito, Kazufumi 1954- Verfasser (DE-588)134247477 aut Evolution equations and approximations Kazufumi Ito ; Franz Kappel River Edge, NJ [u.a.] World Scientific 2002 XIII, 498 S. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 61 Approximation, Théorie de l' Équations d'évolution - Solutions numériques Approximation theory Evolution equations Numerical solutions Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s DE-604 Approximationstheorie (DE-588)4120913-8 s Kappel, Franz 1940- Sonstige (DE-588)124150101 oth Series on advances in mathematics for applied sciences 61 (DE-604)BV004569239 61 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009887734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ito, Kazufumi 1954- Evolution equations and approximations Series on advances in mathematics for applied sciences Approximation, Théorie de l' Équations d'évolution - Solutions numériques Approximation theory Evolution equations Numerical solutions Approximationstheorie (DE-588)4120913-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4129061-6 |
| title | Evolution equations and approximations |
| title_auth | Evolution equations and approximations |
| title_exact_search | Evolution equations and approximations |
| title_full | Evolution equations and approximations Kazufumi Ito ; Franz Kappel |
| title_fullStr | Evolution equations and approximations Kazufumi Ito ; Franz Kappel |
| title_full_unstemmed | Evolution equations and approximations Kazufumi Ito ; Franz Kappel |
| title_short | Evolution equations and approximations |
| title_sort | evolution equations and approximations |
| topic | Approximation, Théorie de l' Équations d'évolution - Solutions numériques Approximation theory Evolution equations Numerical solutions Approximationstheorie (DE-588)4120913-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Approximation, Théorie de l' Équations d'évolution - Solutions numériques Approximation theory Evolution equations Numerical solutions Approximationstheorie Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009887734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004569239 |
| work_keys_str_mv | AT itokazufumi evolutionequationsandapproximations AT kappelfranz evolutionequationsandapproximations |