Hyperbolic conservation laws in continuum physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
325 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 626 S. Ill., graph. Darst. |
| ISBN: | 3540254528 9783540254522 |
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Datensatz im Suchindex
| _version_ | 1804133583463383040 |
|---|---|
| adam_text | CONSTANTINE M. DAFERMOS HYBERBOLIC CONSERVATION LAWS IN CONTINUUM
PHYSICS SECOND EDITION WITH 38 FIGURES 4Y SPRINGER CONTENTS I BALANCE
LAWS 1 1.1 FORMULATION OF THE BALANCE LAW 2 1.2 REDUCTION TO FIELD
EQUATIONS 2 1.3 CHANGE OF COORDINATES AND A TRACE THEOREM 6 1.4 SYSTEMS
OF BALANCE LAWS 11 1.5 COMPANION BALANCE LAWS 12 1.6 WEAK AND SHOCK
FRONTS 15 1.7 SURVEY OF THE THEORY OF BV FUNCTIONS 16 1.8 BV SOLUTIONS
OF SYSTEMS OF BALANCE LAWS 20 1.9 RAPID OSCILLATIONS AND THE STABILIZING
EFFECT OF COMPANION BALANCE LAWS 22 1.10 NOTES : 23 II INTRODUCTION TO
CONTINUUM PHYSICS 25 2.1 BODIES AND MOTIONS . 25 2.2 BALANCE LAWS IN
CONTINUUM PHYSICS 28 2.3 THE BALANCE LAWS OF CONTINUUM THERMOMECHANICS
31 2.4 MATERIAL FRAME INDIFFERENCE 35 2.5 THERMOELASTICITY 36 2.6
THERMOVISCOELASTICITY 43 2.7 INCOMPRESSIBILITY 46 2.8 RELAXATION 47 2.9
NOTES P- 48 III HYPERBOLIC SYSTEMS OF BALANCE LAWS 51 3.1 HYPERBOLICITY
51 3.2 ENTROPY-ENTROPY FLUX PAIRS 52 3.3 EXAMPLES OF HYPERBOLIC SYSTEMS
OF BALANCE LAWS 54 3.4 NOTES 64 XVI CONTENTS IV THE CAUCHY PROBLEM 67
4.1 THE CAUCHY PROBLEM: CLASSICAL SOLUTIONS 67 4.2 BREAKDOWN OF
CLASSICAL SOLUTIONS 70 4.3 THE CAUCHY PROBLEM: WEAK SOLUTIONS 73 4.4
NONUNIQUENESS OF WEAK SOLUTIONS 74 4.5 ENTROPY ADMISSIBILITY CONDITION
75 4.6 THE VANISHING VISCOSITY APPROACH 78 4.7
INITIAL-BOUNDARY-VALUE-PROBLEMS 82 4.8 NOTES 85 V ENTROPY AND THE
STABILITY OF CLASSICAL SOLUTIONS 87 5.1 CONVEX ENTROPY AND THE EXISTENCE
OF CLASSICAL SOLUTIONS 88 5.2 THE ROLE OF DAMPING AND RELAXATION 92 5.3
CONVEX ENTROPY AND THE STABILITY OF CLASSICAL SOLUTIONS 98 5.4
INVOLUTIONS 101 5.5 CONTINGENT ENTROPIES AND POLYCONVEXITY ILL 5.6 NOTES
120 VI THE L 1 THEORY FOR SCALAR CONSERVATION LAWS 123 6.1 THE CAUCHY
PROBLEM: PERSEVERANCE AND DEMISE OF CLASSICAL SOLUTIONS 124 6.2
ADMISSIBLE WEAK SOLUTIONS AND THEIR STABILITY PROPERTIES 126 6.3 THE
METHOD OF VANISHING VISCOSITY 131 6.4 SOLUTIONS AS TRAJECTORIES OF A
CONTRACTION SEMIGROUP 136 6.5 THE LAYERING METHOD 142 6.6 RELAXATION 146
6.7 A KINETIC FORMULATION 153 6.8 FINE STRUCTURE OF L SOLUTIONS 159
6.9 INITIAL-BOUNDARY-VALUE PROBLEMS 162 6.10 THE L 1 THEORY FOR SYSTEMS
OF CONSERVATION LAWS 166 6.11 NOTES 170 VII HYPERBOLIC SYSTEMS OF
BALANCE LAWS IN ONE-SPACE DIMENSION .... 173 7.1 BALANCE LAWS IN
ONE-SPACE DIMENSION 173 7.2 HYPERBOLICITY AND STRICT HYPERBOLICITY 180
7.3 RIEMANN INVARIANTS 183 7.4 ENTROPY-ENTROPY FLUX PAIRS 188 7.5
GENUINE NONLINEARITY AND LINEAR DEGENERACY 190 7.6 SIMPLE WAVES 192 7.7
EXPLOSION OF WEAK FRONTS 197 7.8 BREAKDOWN OF CLASSICAL SOLUTIONS 198
7.9 WEAK SOLUTIONS 201 7.10 NOTES 202 CONTENTS XVII VIII ADMISSIBLE
SHOCKS 205 8.1 STRONG SHOCKS, WEAK SHOCKS, AND SHOCKS OF MODERATE
STRENGTH 205 8.2 THE HUGONIOT LOCUS 207 8.3 THE LAX SHOCK ADMISSIBILITY
CRITERION; COMPRESSIVE, OVERCOMPRESSIVE AND UNDERCOMPRESSIVE SHOCKS .
213 8.4 THE LIU SHOCK ADMISSIBILITY CRITERION 218 8.5 THE ENTROPY SHOCK
ADMISSIBILITY CRITERION 220 8.6 VISCOUS SHOCK PROFILES 224 8.7
NONCONSERVATIVE SHOCKS 234 8.8 NOTES 235 IX ADMISSIBLE WAVE FANS AND THE
RIEMANN PROBLEM 239 9.1 SELF-SIMILAR SOLUTIONS AND THE RIEMANN PROBLEM
239 9.2 WAVE FAN ADMISSIBILITY CRITERIA 242 9.3 SOLUTION OF THE RIEMANN
PROBLEM VIA WAVE FAN CURVES 243 9.4 SYSTEMS WITH GENUINELY NONLINEAR OR
LINEARLY DEGENERATE CHARACTERISTIC FAMILIES 246 9.5 GENERAL STRICTLY
HYPERBOLIC SYSTEMS 248 9.6 FAILURE OF EXISTENCE OR UNIQUENESS; DELTA
SHOCKS AND TRANSITIONAL WAVES 253 9.7 THE ENTROPY RATE ADMISSIBILITY
CRITERION 256 9.8 VISCOUS WAVE FANS 263 9.9 INTERACTION OF WAVE FANS
274 9.10 BREAKDOWN OF WEAK SOLUTIONS 281 9.11 SELF-SIMILAR SOLUTIONS FOR
MULTIDIMENSIONAL CONSERVATION LAWS 285 9.12 NOTES . 289 X GENERALIZED
CHARACTERISTICS 295 10.1 BV SOLUTIONS ... 295 10.2 GENERALIZED
CHARACTERISTICS 296 10.3 EXTREMAL BACKWARD CHARACTERISTICS 298 10.4
NOTES 300 XI GENUINELY NONLINEAR SCALAR CONSERVATION LAWS 301 11.1
ADMISSIBLE B V SOLUTIONS AND GENERALIZED CHARACTERISTICS 302 11.2 THE
SPREADING OF RAREFACTION WAVES 305 11.3 REGULARITY OF SOLUTIONS ? 306
11.4 DIVIDES, INVARIANTS AND THE LAX FORMULA 311 11.5 DECAY OF SOLUTIONS
INDUCED BY ENTROPY DISSIPATION 314 11.6 SPREADING OF CHARACTERISTICS AND
DEVELOPMENT OF N -WAVES .... 316 11.7 CONFINEMENT OF CHARACTERISTICS AND
FORMATION OF SAW-TOOTHED PROFILES 318 11.8 COMPARISON THEOREMS AND L 1
STABILITY 320 11.9 GENUINELY NONLINEAR SCALAR BALANCE LAWS 328 XVIII
CONTENTS 11.10 BALANCE LAWS WITH LINEAR EXCITATION 332 11.11 AN
INHOMOGENEOUS CONSERVATION LAW 335 11.12 NOTES 340 XII GENUINELY
NONLINEAR SYSTEMS OF TWO CONSERVATION LAWS 343 12.1 NOTATION AND
ASSUMPTIONS 343 12.2 ENTROPY-ENTROPY FLUX PAIRS AND THE HODOGRAPH
TRANSFORMATION 345 12.3 LOCAL STRUCTURE OF SOLUTIONS 348 12.4
PROPAGATION OF RIEMANN INVARIANTS ALONG EXTREMAL BACKWARD
CHARACTERISTICS 351 12.5 BOUNDS ON SOLUTIONS 368 12.6 SPREADING OF
RAREFACTION WAVES 381 12.7 REGULARITY OF SOLUTIONS 386 12.8 INITIAL DATA
IN L 1 388 12.9 INITIAL DATA WITH COMPACT SUPPORT 392 12.10 PERIODIC
SOLUTIONS 398 12.11 NOTES 403 XIII THE RANDOM CHOICE METHOD 405 13.1 THE
CONSTRUCTION SCHEME 405 13.2 COMPACTNESS AND CONSISTENCY ...: 408 13.3
WAVE INTERACTIONS, APPROXIMATE CONSERVATION LAWS AND APPROXIMATE
CHARACTERISTICS IN GENUINELY NONLINEAR SYSTEMS 414 13.4 THE GLIMM
FUNCTIONAL FOR GENUINELY NONLINEAR SYSTEMS 418 13.5 BOUNDS ON THE TOTAL
VARIATION FOR GENUINELY NONLINEAR SYSTEMS 423 13.6 BOUNDS ON THE
SUPREMUM FOR GENUINELY NONLINEAR SYSTEMS ... 425 13.7 GENERAL SYSTEMS ,
428 13.8 WAVE TRACING 430 13.9 INHOMOGENEOUS SYSTEMS OF BALANCE LAWS 433
13.10 NOTES 440 XIV THE FRONT TRACKING METHOD AND STANDARD RIEMANN
SEMIGROUPS .. 443 14.1 FRONT TRACKING FOR SCALAR CONSERVATION LAWS 444
14.2 FRONT TRACKING FOR GENUINELY NONLINEAR SYSTEMS OF CONSERVATION LAWS
447 14.3 THE GLOBAL WAVE PATTERN * 451 14.4 APPROXIMATE SOLUTIONS 452
14.5 BOUNDS ON THE TOTAL VARIATION 455 14.6 BOUNDS ON THE COMBINED
STRENGTH OF PSEUDOSHOCKS 458 14.7 COMPACTNESS AND CONSISTENCY 460 14.8
CONTINUOUS DEPENDENCE ON INITIAL DATA 462 14.9 THE STANDARD RIEMANN
SEMIGROUP 466 14.10 UNIQUENESS OF SOLUTIONS 468 CONTENTS XIX 14.11
CONTINUOUS GLIMM FUNCTIONALS, SPREADING OF RAREFACTION WAVES, AND
STRUCTURE OF SOLUTIONS 473 14.12 STABILITY OF STRONG WAVES 476 14.13
NOTES 479 XV CONSTRUCTION OF B V SOLUTIONS BY THE VANISHING VISCOSITY
METHOD .. 483 15.1 THE MAIN RESULT 483 15.2 ROAD MAP TO THE PROOF OF
THEOREM 15.1.1 485 15.3 THE EFFECTS OF DIFFUSION 487 15.4 DECOMPOSITION
INTO VISCOUS TRAVELING WAVES 490 15.5 TRANSVERSAL WAVE INTERACTIONS 494
15.6 INTERACTION OF WAVES OF THE SAME FAMILY 498 15.7 ENERGY ESTIMATES
503 15.8 STABILITY ESTIMATES 506 15.9 NOTES 508 XVI COMPENSATED
COMPACTNESS 511 16.1 THE YOUNG MEASURE 512 16.2 COMPENSATED COMPACTNESS
AND THE DIV-CURL LEMMA 513 16.3 MEASURE-VALUED SOLUTIONS FOR SYSTEMS OF
CONSERVATION LAWS AND COMPENSATED COMPACTNESS 515 16.4 SCALAR
CONSERVATION LAWS 518 16.5 A RELAXATION SCHEME FOR SCALAR CONSERVATION
LAWS 519 16.6 GENUINELY NONLINEAR SYSTEMS OF TWO CONSERVATION LAWS 523
16.7 THE SYSTEM OF ISENTROPIC ELASTICITY 525 16.8 THE SYSTEM OF
ISENTROPIC GAS DYNAMICS 530 16.9 NOTES 533 BIBLIOGRAPHY 53 7 AUTHOR
INDEX 613 SUBJECT INDEX 621
|
| any_adam_object | 1 |
| author | Dafermos, Constantine M. 1941- |
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| author_facet | Dafermos, Constantine M. 1941- |
| author_role | aut |
| author_sort | Dafermos, Constantine M. 1941- |
| author_variant | c m d cm cmd |
| building | Verbundindex |
| bvnumber | BV020021281 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.3.C58 |
| callnumber-search | QC793.3.C58 |
| callnumber-sort | QC 3793.3 C58 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 |
| classification_tum | PHY 210f PHY 013f MAT 357f |
| ctrlnum | (OCoLC)254564179 (DE-599)BVBBV020021281 |
| dewey-full | 530.1553535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1553535 |
| dewey-search | 530.1553535 |
| dewey-sort | 3530.1553535 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | 1\p (DE-588)4179998-7 Monografische Reihe gnd-content |
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| id | DE-604.BV020021281 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:11:01Z |
| institution | BVB |
| isbn | 3540254528 9783540254522 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013342647 |
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| publisher | Springer |
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| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Dafermos, Constantine M. 1941- Verfasser (DE-588)121360229 aut Hyperbolic conservation laws in continuum physics Constantine M. Dafermos 2. ed. Berlin [u.a.] Springer 2005 XIX, 626 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 325 Kontinuumsphysik - Erhaltungssatz - Hyperbolisches System Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Kontinuumsphysik (DE-588)4165166-2 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf 1\p (DE-588)4179998-7 Monografische Reihe gnd-content Erhaltungssatz (DE-588)4131214-4 s Hyperbolische Differentialgleichung (DE-588)4131213-2 s Kontinuumsphysik (DE-588)4165166-2 s DE-604 Hyperbolisches System (DE-588)4191897-6 s 2\p DE-604 Die Grundlehren der mathematischen Wissenschaften 325 (DE-604)BV000000395 325 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013342647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dafermos, Constantine M. 1941- Hyperbolic conservation laws in continuum physics Die Grundlehren der mathematischen Wissenschaften Kontinuumsphysik - Erhaltungssatz - Hyperbolisches System Hyperbolisches System (DE-588)4191897-6 gnd Kontinuumsphysik (DE-588)4165166-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4191897-6 (DE-588)4165166-2 (DE-588)4131214-4 (DE-588)4131213-2 (DE-588)4179998-7 |
| title | Hyperbolic conservation laws in continuum physics |
| title_auth | Hyperbolic conservation laws in continuum physics |
| title_exact_search | Hyperbolic conservation laws in continuum physics |
| title_full | Hyperbolic conservation laws in continuum physics Constantine M. Dafermos |
| title_fullStr | Hyperbolic conservation laws in continuum physics Constantine M. Dafermos |
| title_full_unstemmed | Hyperbolic conservation laws in continuum physics Constantine M. Dafermos |
| title_short | Hyperbolic conservation laws in continuum physics |
| title_sort | hyperbolic conservation laws in continuum physics |
| topic | Kontinuumsphysik - Erhaltungssatz - Hyperbolisches System Hyperbolisches System (DE-588)4191897-6 gnd Kontinuumsphysik (DE-588)4165166-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Kontinuumsphysik - Erhaltungssatz - Hyperbolisches System Hyperbolisches System Kontinuumsphysik Erhaltungssatz Hyperbolische Differentialgleichung Monografische Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013342647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT dafermosconstantinem hyperbolicconservationlawsincontinuumphysics |