Hyperbolic conservation laws in continuum physics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
[2016]
|
| Edition: | Fourth edition |
| Series: | Grundlehren der mathematischen Wissenschaften
volume 325 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXXVIII, 826 Seiten Illustrationen, Diagramme |
| ISBN: | 9783662494493 9783662494516 3662494493 |
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| 653 | |a mechanics | ||
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Record in the Search Index
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|---|---|
| adam_text |
Constantine M Dafermos
Hyperbolic Conservation
Laws in Continuum Physics
Fourth Edition
£) Springer
■
ly
'■
■1-, ---------
Contents
4
;$'r'
'- '
,*• I Balance Laws 1
j11 Formulation of the Balance Law 2
|12 Reduction to Field Equations 3
|y 1 3 Change of Coordinates and a Trace Theorem 7
f14 Systems of Balance Laws 12
1 5 Companion Balance Laws 13
ff 1 6 Weak and Shock Fronts 15
1 7 Survey of the Theory of BV Functions 17
|18 Resolutions of Systems of Balance Laws 21
f19 Rapid Oscillations and the Stabilizing Effect of Companion
Balance Laws 23
1 10 Notes 23
I II Introduction to Continuum Physics 25
f21 Kinematics 25
I22 Balance Laws in Continuum Physics 28
|23 The Balance Laws of Continuum Thermomechanics 31
|24 Material Frame Indifference 35
|25 Thermoelasticity 36
|26 Thermoviscoelasticity 44
|27 Incompressibility 47
;28 Relaxation 48
{29 Notes ' 49
§ III Hyperbolic Systems of Balance Laws 53
I31 Hyperbolicity 53
;32 Entropy-Entropy Flux Pairs 54
|33 Examples of Hyperbolic Systems of Balance Laws 56
I34 Notes 73
XXXIV Contents
IV The Cauchy Problem 77
4 1 The Cauchy Problem: Classical Solutions 77
4 2 Breakdown of Classical Solutions 80
4 3 The Cauchy Problem: Weak Solutions 82
4 4 Nonuniqueness of Weak Solutions 83
4 5 Entropy Admissibility Condition 84
4 6 The Vanishing Viscosity Approach 90
4 7 Initial-Boundary Value Problems 94
4 8 Euler Equations 97
4 9 Notes 107
V Entropy and the Stability of Classical Solutions Ill
5 1 Convex Entropy and the Existence of Classical Solutions 112
5 2 Relative Entropy and the Stability of Classical Solutions 122
5 3 Involutions and Contingent Entropies 125
5 4 Contingent Entropies and Polyconvexity 138
5 5 The Role of Damping and Relaxation 146
5 6 Initial-Boundary Value Problems 160
5 7 Notes 170
VI The L1 Theory for Scalar Conservation Laws 175
6 1 The Cauchy Problem: Perseverance and Demise
of Classical Solutions 176
6 2 Admissible Weak Solutions and their Stability Properties 178
6 3 The Method of Vanishing Viscosity 183
6 4 Solutions as Trajectories of a Contraction Semigroup and the
Large Time Behavior of Periodic Solutions 188
6 5 The Layering Method 195
6 6 Relaxation 199
67A Kinetic Formulation 205
6 8 Fine Structure of L°° Solutions 212
6 9 Initial-Boundary Value Problems 215
6 10 The L1 Theory for Systems of Conservation Laws 220
6 11 Notes 223
VII Hyperbolic Systems of Balance Laws
in One-Space Dimension 227
7 1 Balance Laws in One-Space Dimension 227
7 2 Hyperbolicity and Strict Hyperbolicity 235
7 3 Riemann Invariants 238
7 4 Entropy-Entropy Flux Pairs 243
7 5 Genuine Nonlinearity and Linear Degeneracy 245
7 6 Simple Waves 247
7 7 Explosion of Weak Fronts 252
7 8 Existence and Breakdown of Classical Solutions 253
7 9 Weak Solutions 257
Contents XXXV
Vffl
7 10 Notes 258
Admissible Shocks 263
8 1 Strong Shocks, Weak Shocks, and Shocks of Moderate Strength 263
8 2 The Hugoniot Locus 266
8 3 The Lax Shock Admissibility Criterion;
Compressive, Overcompressive and Undercompressive Shocks 272
8 4 The Liu Shock Admissibility Criterion 278
8 5 The Entropy Shock Admissibility Criterion 280
8 6 Viscous Shock Profiles 285
8 7 Nonconservative Shocks 296
8 8 Notes 297
Admissible Wave Fans and the Riemann Problem 303
9 1 Self-Similar Solutions and the Riemann Problem 303
9 2 Wave Fan Admissibility Criteria 307
9 3 Solution of the Riemann Problem via Wave Curves 309
9 4 Systems with Genuinely Nonlinear
or Linearly Degenerate Characteristic Families 312
9 5 General Strictly Hyperbolic Systems 316
9 6 Failure of Existence or Uniqueness;
Delta Shocks and Transitional Waves 320
9 7 The Entropy Rate Admissibility Criterion 323
9 8 Viscous Wave Fans 332
9 9 Interaction of Wave Fans 343
9 10 Breakdown of Weak Solutions 350
9 11 Notes 354
Generalized Characteristics 359
10 1 BV Solutions 359
10 2 Generalized Characteristics 360
10 3 Extremal Backward Characteristics 362
10 4 Notes 365
Scalar Conservation Laws in One Space Dimension 367
11 1 Admissible BV Solutions and Generalized Characteristics 368
11 2 The Spreading of Rarefaction Waves 371
11 3 Regularity of Solutions 372
11 4 Divides, Invariants and the Lax Formula 377
11 5 Decay of Solutions Induced by Entropy Dissipation 380
11 6 Spreading of Characteristics and Development of N- Waves 383
11 7 Confinement of Characteristics
and Formation of Saw-toothed Profiles 384
11 8 Comparison Theorems and L1 Stability 386
11 9 Genuinely Nonlinear Scalar Balance Laws 395
11 10 Balance Laws with Linear Excitation 399
■
XXXVI Contents
11 11 An Inhomogeneous Conservation Law 401
11 12 When Genuine Nonlinearity Fails 406
11 13 Entropy Production 418
11 14 Notes 422
Xn Genuinely Nonlinear Systems of Two Conservation Laws 427
12 1 Notation and Assumptions 427
12 2 Entropy-Entropy Flux Pairs and the Hodograph Transformation 429
12 3 Local Structure of Solutions 432
12 4 Propagation of Riemann Invariants
Along Extremal Backward Characteristics 435
12 5 Bounds on Solutions 452
12 6 Spreading of Rarefaction Waves 464
12 7 Regularity of Solutions 469
12 8 Initial Data in L1 471
12 9 Initial Data with Compact Support 475
12 10 Periodic Solutions 481
12 11 Notes 486
XIII The Random Choice Method 489
13 1 The Construction Scheme 489
13 2 Compactness and Consistency 492
13 3 Wave Interactions in Genuinely Nonlinear Systems 498
13 4 The Glimm Functional for Genuinely Nonlinear Systems 500
13 5 Bounds on the Total Variation
for Genuinely Nonlinear Systems 505
13 6 Bounds on the Supremum for Genuinely Nonlinear Systems 507
13 7 General Systems 509
13 8 Wave Tracing 512
13 9 Notes 515
XIV The Front Tracking Method and Standard Riemann Semigroups 517
14 1 Front Tracking for Scalar Conservation Laws 518
14 2 Front Tracking for Genuinely Nonlinear
Systems of Conservation Laws 520
14 3 The Global Wave Pattern 525
14 4 Approximate Solutions 526
14 5 Bounds on the Total Variation 528
14 6 Bounds on the Combined Strength of Pseudoshocks 531
14 7 Compactness and Consistency 534
14 8 Continuous Dependence on Initial Data 536
14 9 The Standard Riemann Semigroup 540
14 10 Uniqueness of Solutions 541
14 11 Continuous Glimm Functionals,
Spreading of Rarefaction Waves,
and Structure of Solutions 547
Contents XXXVII
14 12 Stability of Strong Waves 550
14 13 Notes 552
Construction of BV Solutions by the Vanishing Viscosity Method 557
15 1 The Main Result 557
15 2 Road Map to the Proof of Theorem 15 1 1 559
15 3 The Effects of Diffusion 561
15 4 Decomposition into Viscous Traveling Waves 564
15 5 Transversal Wave Interactions 568
15 6 Interaction of Waves of the Same Family 572
15 7 Energy Estimates 576
15 8 Stability Estimates 579
15 9 Notes 582
BV Solutions for Systems of Balance Laws 585
16 1 The Cauchy Problem 586
16 2 Strong Dissipation 589
16 3 Redistribution of Damping 593
16 4 Bounds on the Variation 595
16 5 L1 Stability Via Entropy with Conical Singularity at the Origin 606
16 6 L1 Stability when the Source is Partially Dissipative 609
16 7 Notes 622
Compensated Compactness 623
17 1 The Young Measure 624
17 2 Compensated Compactness and the div-curl Lemma 625
17 3 Measure-Valued Solutions for Systems of Conservation Laws
and Compensated Compactness 626
17 4 Scalar Conservation Laws 629
17 5 A Relaxation Scheme for Scalar Conservation Laws 631
17 6 Genuinely Nonlinear Systems of Two Conservation Laws 634
17 7 The System of Isentropic Elasticity 637
17 8 The System of Isentropic Gas Dynamics 642
17 9 Notes 648
XVni Steady and Self-similar Solutions in Multi-Space Dimensions 655
18 1 Self-Similar Solutions for Multidimensional Scalar
Conservation Laws 655
18 2 Steady Planar Isentropic Gas Flow 658
18 3 Self-Similar Planar Irrotational Isentropic Gas Flow 663
18 4 Supersonic Isentropic Gas Flow Past a Ramp 667
18 5 Regular Shock Reflection on a Wall 672
18 6 Shock Collision with a Ramp 675
18 7 Isometric Immersions 678
18 8 Cavitation in Elastodynamics 682
18 9 Notes 686
XXXVIII Contents
Bibliography 691
Author Index 811 |
| 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 |
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| bvnumber | BV043675856 |
| classification_rvk | SK 540 SK 560 SK 950 |
| ctrlnum | (OCoLC)952224313 (DE-599)DNB1103510266 |
| dewey-full | 530.1553535 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics 510 - Mathematics |
| dewey-raw | 530.1553535 510 |
| dewey-search | 530.1553535 510 |
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| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | Fourth edition |
| format | Book |
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| 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 Fourth edition Berlin Springer [2016] © 2016 XXXVIII, 826 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften volume 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 aerodynamics conservation laws continuum mechanics entropy hypberbolic systems mechanics partial differential equations shock waves stability thermodynamics (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 1\p DE-604 Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 10.1007/978-3-662-49451-6 Grundlehren der mathematischen Wissenschaften volume 325 (DE-604)BV000000395 325 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=75c166add3cd4227b0b307ab17654e9b&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029088874&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 |
| 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=75c166add3cd4227b0b307ab17654e9b&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=029088874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT dafermosconstantinem hyperbolicconservationlawsincontinuumphysics AT springerverlaggmbh hyperbolicconservationlawsincontinuumphysics |