Hyperbolic conservation laws in continuum physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg u. a.
Springer
2010
|
| Edition: | 3. ed. |
| Series: | Grundlehren der mathematischen Wissenschaften
325 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXXV, 708 S. |
| ISBN: | 9783642040474 9783642040481 |
Staff View
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Record in the Search Index
| _version_ | 1805093143330160640 |
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| adam_text |
IMAGE 1
CONTENTS
I BALANCE LAWS 1
1.1 FORMULATION OF THE BALANCE LAW 2
1.2 REDUCTION TO FIELD EQUATIONS 3
1.3 CHANGE OF COORDINATES AND A TRACE THEOREM 7
1.4 SYSTEMS OF BALANCE LAWS 12
1.5 COMPANION BALANCE LAWS 13
1.6 WEAK AND SHOCK FRONTS 15
1.7 SURVEY OF THE THEORY OF .OF FUNCTIONS 17
1.8 BV SOLUTIONS OF SYSTEMS OF BALANCE LAWS 21
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 44
2.7 INCOMPRESSIBILITY 47
2.8 RELAXATION 48
2.9 NOTES 49
III HYPERBOLIC SYSTEMS OF BALANCE LAWS 53
3.1 HYPERBOLICITY 53
3.2 ENTROPY-ENTROPY FLUX PAIRS 54
3.3 EXAMPLES OF HYPERBOLIC SYSTEMS OF BALANCE LAWS 56
3.4 NOTES 72
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995796157
DIGITALISIERT DURCH
IMAGE 2
XXXII CONTENTS
IV THE CAUCHY PROBLEM 75
4.1 THE CAUCHY PROBLEM: CLASSICAL SOLUTIONS 75
4.2 BREAKDOWN OF CLASSICAL SOLUTIONS 78
4.3 THE CAUCHY PROBLEM: WEAK SOLUTIONS 81
4.4 NONUNIQUENESS OF WEAK SOLUTIONS 82
4.5 ENTROPY ADMISSIBILITY CONDITION 83
4.6 THE VANISHING VISCOSITY APPROACH 87
4.7 INITIAL-BOUNDARY VALUE PROBLEMS 91
4.8 NOTES 95
V ENTROPY AND THE STABILITY OF CLASSICAL SOLUTIONS 97
5. 1 CONVEX ENTROPY AND THE EXISTENCE OF CLASSICAL SOLUTIONS 98 5.2 THE
ROLE OF DAMPING AND RELAXATION 108
5.3 CONVEX ENTROPY AND THE STABILITY OF CLASSICAL SOLUTIONS 116 5.4
INVOLUTIONS 119
5.5 CONTINGENT ENTROPIES AND POLYCONVEXITY 129
5.6 INITIAL-BOUNDARY VALUE PROBLEMS 138
5.7 NOTES 141
VI THE U THEORY FOR SCALAR CONSERVATION LAWS 145
6. 1 THE CAUCHY PROBLEM: PERSEVERANCE AND DEMISE OF CLASSICAL SOLUTIONS
146
6.2 ADMISSIBLE WEAK SOLUTIONS AND THEIR STABILITY PROPERTIES 148 6.3 THE
METHOD OF VANISHING VISCOSITY 153
6.4 SOLUTIONS AS TRAJECTORIES OF A CONTRACTION SEMIGROUP 158 6.5 THE
LAYERING METHOD 164
6.6 RELAXATION 167
6.7 A KINETIC FORMULATION 174
6.8 FINE STRUCTURE OF L SOLUTIONS 180
6.9 INITIAL-BOUNDARY VALUE PROBLEMS 183
6.10 THE L 1 THEORY FOR SYSTEMS OF CONSERVATION LAWS 188
6.11 NOTES 192
VII HYPERBOLIC SYSTEMS OF BALANCE LAWS IN ONE-SPACE DIMENSION 195
7. 1 BALANCE LAWS IN ONE-SPACE DIMENSION 195
7.2 HYPERBOLICITY AND STRICT HYPERBOLICITY 203
7.3 RIEMANN INVARIANTS 206
7.4 ENTROPY-ENTROPY FLUX PAIRS 211
7.5 GENUINE NONLINEARITY AND LINEAR DEGENERACY 214
7.6 SIMPLE WAVES 216
7.7 EXPLOSION OF WEAK FRONTS 220
7.8 EXISTENCE AND BREAKDOWN OF CLASSICAL SOLUTIONS 221
7.9 WEAK SOLUTIONS 225
7.10 NOTES 226
IMAGE 3
CONTENTS XXXIII
VIII ADMISSIBLE SHOCKS 231
8.1 STRONG SHOCKS, WEAK SHOCKS, AND SHOCKS OF MODERATE STRENGTH 231 8.2
THE HUGONIOT LOCUS 234
8.3 THE LAX SHOCK ADMISSIBILITY CRITERION; COMPRESSIVE, OVERCOMPRESSIVE
AND UNDERCOMPRESSIVE SHOCKS . 240 8.4 THE LIU SHOCK ADMISSIBILITY
CRITERION 246
8.5 THE ENTROPY SHOCK ADMISSIBILITY CRITERION 248
8.6 VISCOUS SHOCK PROFILES 252
8.7 NONCONSERVATIVE SHOCKS 264
8.8 NOTES 265
IX ADMISSIBLE WAVE FANS AND THE RIEMANN PROBLEM 271
9.1 SELF-SIMILAR SOLUTIONS AND THE RIEMANN PROBLEM 271
9.2 WAVE FAN ADMISSIBILITY CRITERIA 274
9.3 SOLUTION OF THE RIEMANN PROBLEM VIA WAVE CURVES 275 9.4 SYSTEMS WITH
GENUINELY NONLINEAR OR LINEARLY DEGENERATE CHARACTERISTIC FAMILIES 278
9.5 GENERAL STRICTLY HYPERBOLIC SYSTEMS 283
9.6 FAILURE OF EXISTENCE OR UNIQUENESS; DELTA SHOCKS AND TRANSITIONAL
WAVES 287
9.7 THE ENTROPY RATE ADMISSIBILITY CRITERION 290
9.8 VISCOUS WAVE FANS 299
9.9 INTERACTION OF WAVE FANS 309
9.10 BREAKDOWN OF WEAK SOLUTIONS 317
9.11 NOTES 320
X GENERALIZED CHARACTERISTICS 325
10.1 V SOLUTIONS 325
10.2 GENERALIZED CHARACTERISTICS 326
10.3 EXTREMAL BACKWARD CHARACTERISTICS 328
10.4 NOTES 330
XI GENUINELY NONLINEAR SCALAR CONSERVATION LAWS 331
11.1 ADMISSIBLE BV SOLUTIONS AND GENERALIZED CHARACTERISTICS 332 11.2
THE SPREADING OF RAREFACTION WAVES 335
11.3 REGULARITY OF SOLUTIONS 336
11.4 DIVIDES, INVARIANTS AND THE LAX FORMULA 340
11.5 DECAY OF SOLUTIONS INDUCED BY ENTROPY DISSIPATION 344 11.6
SPREADING OF CHARACTERISTICS AND DEVELOPMENT OF N- WAVES 346 11.7
CONFINEMENT OF CHARACTERISTICS AND FORMATION OF SAW-TOOTHED PROFILES 348
11.8 COMPARISON THEOREMS AND U STABILITY 350
11.9 GENUINELY NONLINEAR SCALAR BALANCE LAWS 358
11.10 BALANCE LAWS WITH LINEAR EXCITATION 362
11.11 AN INHOMOGENEOUS CONSERVATION LAW 365
11.12 NOTES 370
IMAGE 4
XXXIV CONTENTS
XII GENUINELY NONLINEAR SYSTEMS OF TWO CONSERVATION LAWS 373 12. 1
NOTATION AND ASSUMPTIONS 373
12.2 ENTROPY-ENTROPY FLUX PAIRS AND THE HODOGRAPH TRANSFORMATION 375
12.3 LOCAL STRUCTURE OF SOLUTIONS 378
12.4 PROPAGATION OF RIEMANN INVARIANTS ALONG EXTREMAL BACKWARD
CHARACTERISTICS 381
12.5 BOUNDS ON SOLUTIONS 398
12.6 SPREADING OF RAREFACTION WAVES 410
12.7 REGULARITY OF SOLUTIONS 415
12.8 INITIAL DATA IN L 1 417
12.9 INITIAL DATA WITH COMPACT SUPPORT 421
12.10 PERIODIC SOLUTIONS 427
12.11 NOTES 432
XIII THE RANDOM CHOICE METHOD 435
13.1 THE CONSTRUCTION SCHEME 435
13.2 COMPACTNESS AND CONSISTENCY 438
13.3 WAVE INTERACTIONS, APPROXIMATE CONSERVATION LAWS AND APPROXIMATE
CHARACTERISTICS IN GENUINELY NONLINEAR SYSTEMS 444
13.4 THE GLIMM FUNCTIONAL FOR GENUINELY NONLINEAR SYSTEMS 448 13.5
BOUNDS ON THE TOTAL VARIATION FOR GENUINELY NONLINEAR SYSTEMS 453
13.6 BOUNDS ON THE SUPREMUM FOR GENUINELY NONLINEAR SYSTEMS . . 455
13.7 GENERAL SYSTEMS 457
13.8 WAVE TRACING 460
13.9 INHOMOGENEOUS SYSTEMS OF BALANCE LAWS 463
13.10 NOTES 474
XIV THE FRONT TRACKING METHOD AND STANDARD RIEMANN SEMIGROUPS . 477
14.1 FRONT TRACKING FOR SCALAR CONSERVATION LAWS 478
14.2 FRONT TRACKING FOR GENUINELY NONLINEAR SYSTEMS OF CONSERVATION LAWS
480
14.3 THE GLOBAL WAVE PATTERN 485
14.4 APPROXIMATE SOLUTIONS 486
14.5 BOUNDS ON THE TOTAL VARIATION 488
14.6 BOUNDS ON THE COMBINED STRENGTH OF PSEUDOSHOCKS 491 14.7
COMPACTNESS AND CONSISTENCY 494
14.8 CONTINUOUS DEPENDENCE ON INITIAL DATA 496
14.9 THE STANDARD RIEMANN SEMIGROUP 500
14.10 UNIQUENESS OF SOLUTIONS 501
14.11 CONTINUOUS GLIMM FUNCTIONALS, SPREADING OF RAREFACTION WAVES, AND
STRUCTURE OF SOLUTIONS 507
14.12 STABILITY OF STRONG WAVES 510
14.13 NOTES 512
IMAGE 5
CONTENTS XXXV
XV CONSTRUCTION OF BV SOLUTIONS BY THE VANISHING VISCOSITY METHOD . 517
15.1 THE MAIN RESULT 517
15.2 ROAD MAP TO THE PROOF OF THEOREM 15.1.1 519
15.3 THE EFFECTS OF DIFFUSION 521
15.4 DECOMPOSITION INTO VISCOUS TRAVELING WAVES 524
15.5 TRANSVERSAL WAVE INTERACTIONS 528
15.6 INTERACTION OF WAVES OF THE SAME FAMILY 532
15.7 ENERGY ESTIMATES 536
15.8 STABILITY ESTIMATES 539
15.9 NOTES 542
XVI COMPENSATED COMPACTNESS 545
16.1 THE YOUNG MEASURE 546
16.2 COMPENSATED COMPACTNESS AND THE DIV-CURL LEMMA 547 16.3
MEASURE-VALUED SOLUTIONS FOR SYSTEMS OF CONSERVATION LAWS AND
COMPENSATED COMPACTNESS 548
16.4 SCALAR CONSERVATION LAWS 551
16.5 A RELAXATION SCHEME FOR SCALAR CONSERVATION LAWS 553 16.6 GENUINELY
NONLINEAR SYSTEMS OF TWO CONSERVATION LAWS 556 16.7 THE SYSTEM OF
ISENTROPIC ELASTICITY 559
16.8 THE SYSTEM OF ISENTROPIC GAS DYNAMICS 564
16.9 NOTES 567
XVII CONSERVATION LAWS IN TWO SPACE DIMENSIONS 573
17.1 SELF-SIMILAR SOLUTIONS FOR MULTIDIMENSIONAL SCALAR CONSERVATION
LAWS 573
17.2 STEADY PLANAR ISENTROPIC GAS FLOW 576
17.3 SELF-SIMILAR PLANAR IRROTATIONAL ISENTROPIC GAS FLOW 580 17.4
SUPERSONIC ISENTROPIC GAS FLOW PAST A RAMP OF GENTLE SLOPE . 583 17.5
REGULAR SHOCK REFLECTION ON A WALL 588
17.6 SHOCK COLLISION WITH A STEEP RAMP 591
17.7 NOTES 594
BIBLIOGRAPHY 597
AUTHOR INDEX 693
SUBJECT INDEX 703 |
| any_adam_object | 1 |
| author | Dafermos, Constantine M. 1941- |
| author_GND | (DE-588)121360229 |
| 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 | BV035804362 |
| classification_rvk | SK 560 SK 950 |
| ctrlnum | (OCoLC)634763534 (DE-599)DNB995796157 |
| 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 | 3. ed. |
| format | Book |
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| indexdate | 2024-07-20T10:22:49Z |
| institution | BVB |
| isbn | 9783642040474 9783642040481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018663435 |
| oclc_num | 634763534 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-11 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 DE-83 |
| owner_facet | DE-703 DE-384 DE-11 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 DE-83 |
| physical | XXXV, 708 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Dafermos, Constantine M. 1941- Verfasser (DE-588)121360229 aut Hyperbolic conservation laws in continuum physics Constantine M. Dafermos 3. ed. Heidelberg u. a. Springer 2010 XXXV, 708 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 325 Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Kontinuumsphysik (DE-588)4165166-2 gnd rswk-swf 1\p (DE-588)4179998-7 Monografische Reihe gnd-content Kontinuumsphysik (DE-588)4165166-2 s Erhaltungssatz (DE-588)4131214-4 s Hyperbolisches System (DE-588)4191897-6 s DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s 2\p DE-604 Grundlehren der mathematischen Wissenschaften 325 (DE-604)BV000000395 325 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3341979&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=018663435&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 Grundlehren der mathematischen Wissenschaften Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Kontinuumsphysik (DE-588)4165166-2 gnd |
| subject_GND | (DE-588)4131213-2 (DE-588)4131214-4 (DE-588)4191897-6 (DE-588)4165166-2 (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 | Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Kontinuumsphysik (DE-588)4165166-2 gnd |
| topic_facet | Hyperbolische Differentialgleichung Erhaltungssatz Hyperbolisches System Kontinuumsphysik Monografische Reihe |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3341979&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018663435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT dafermosconstantinem hyperbolicconservationlawsincontinuumphysics |