连续介质物理中的双曲守恒律 第3版=HYPERBOLIC CONSERVATION LAWS IN CONTINUUM PHYSICS THIRD EDITION 英文PDF|Epub|txt|kindle电子书版本网盘下载

连续介质物理中的双曲守恒律 第3版=HYPERBOLIC CONSERVATION LAWS IN CONTINUUM PHYSICS THIRD EDITION 英文PDF格式电子书版下载

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Ⅰ Balance Laws1

1.1 Formulation of the Balance Law2

1.2 Reduction to Field Equations3

1.3 Change of Coordinates and a Trace Theorem7

1.4 Systems of Balance Laws12

1.5 Companion Balance Laws13

1.6 Weak and Shock Fronts15

1.7 Survey of the Theory of BV Functions17

1.8 BV Solutions of Systems of Balance Laws21

1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws22

1.10 Notes23

Ⅱ Introduction to Continuum Physics25

2.1 Bodies and Motions25

2.2 Balance Laws in Continuum Physics28

2.3 The Balance Laws of Continuum Thermomechanics31

2.4 Material Frame Indifference35

2.5 Thermoelasticity36

2.6 Thermoviscoelasticity44

2.7 Incompressibility47

2.8 Relaxation48

2.9 Notes49

Ⅲ Hyperbolic Systems of Balance Laws53

3.1 Hyperbolicity53

3.2 Entropy-Entropy Flux Pairs54

3.3 Examples of Hyperbolic Systems of Balance Laws56

3.4 Notes72

Ⅳ The Cauchy Problem75

4.1 The Cauchy Problem:Ciassical Solutions75

4.2 Breakdown ofClassical Solutions78

4.3 The Cauchy Problem:Weak Solutions81

4.4 Nonuniqueness of Weak Solutions82

4.5 Entropy Admissibility Condition83

4.6 The Vanishing Viscosity Approach87

4.7 Initial-Boundary Value Problems91

4.8 Notes95

Ⅴ Entropy and the Stability of Classical Solutions97

5.1 Convex Entropy and the Existence of Classical Solutions98

5.2 The Role ofDamping and Relaxation108

5.3 Convex Entropy and the Stability of Classical Solutions116

5.4 Involutions119

5.5 Contingent Entropies and Polyconvexity129

5.6 Initial-Boundary Value Problems138

5.7 Notes141

Ⅵ The L1 Theory for Scalar Conservation Laws145

6.1 The Cauchy Problem:Perseverance and Demise of Classical Solutions146

6.2 Admissible Weak Solutions and their Stability Properties148

6.3 The Method of Vanishing Viscosity153

6.4 Solutions as Trajectories of a Contraction Semigroup158

6.5 The Layering Method164

6.6 Relaxation167

6.7 A Kinetic Formulation174

6.8 Fine Structure of L∞ Solutions180

6.9 Initial-Boundary Value Problems183

6.10 The L1 Theory for Systems of Conservation Laws188

6.11 Notes192

Ⅶ Hyperbolic Systems of Balance Laws in One-Space Dimension195

7.1 Balance Laws in One-Space Dimension195

7.2 Hyperbolicity and Strict Hyperbolicity203

7.3 Riemann Invariants206

7.4 Entropy-Entropy Flux Pairs211

7.5 Genuine Nonlinearity and Linear Degeneracy214

7.6 Simple Waves216

7.7 Explosion of Weak Fronts220

7.8 Existence and Breakdown of Classical Solutions221

7.9 Weak Solutions225

7.10 Notes226

Ⅷ Admissible Shocks231

8.1 Strong Shocks,Weak Shocks,and Shocks of Moderate Strength231

8.2 The Hugoniot Locus234

8.3 The Lax Shock Admissibility Criterion;Compressive,Overcompressive and Undercompressive Shocks240

8.4 The Liu Shock Admissibility Criterion246

8.5 The Entropy Shock Admissibility Criterion248

8.6 Viscous Shock Profiles252

8.7 Nonconservative Shocks264

8.8 Notes265

Ⅸ Admissible Wave Fans and the Riemann Problem271

9.1 Self-Similar Solutions and the Riemann Problem271

9.2 Wave Fan Admissibility Criteria274

9.3 Solution of the Riemann Problem via Wave Curves275

9.4 Systems with Genuinely Nonlinear or Linearly Degenerate Characteristic Families278

9.5 General Strictly Hyperbolic Systems283

9.6 Failure of Existence or Uniqueness;Delta Shocks and Transitional Waves287

9.7 The Entropy Rate Admissibility Criterion290

9.8 Viscous Wave Fans299

9.9 Interaction of Wave Fans309

9.10 Breakdown of Weak Solutions317

9.11 Notes320

Ⅹ Generalized Characteristics325

10.1 BV Solutions325

10.2 Generalized Characteristics326

10.3 Extremal Backward Characteristics328

10.4 Notes330

Ⅺ Genuinely Nonlinear Scalar Conservation Laws331

11.1 Admissible BV Solutions and Generalized Characteristics332

11.2 The Spreading of Rarefaction Waves335

11.3 Regularity of Solutions336

11.4 Divides,Invariants and the Lax Formula340

11.5 Decay of Solutions Induced by Entropy Dissipation344

11.6 Spreading of Characteristics and Development of N-Waves346

11.7 Confinement of Characteristics and Formation of Saw-toothed Profiles348

11.8 Comparison Theorems and L1 Stability350

11.9 Genuinely Nonlinear Scalar Balance Laws358

11.10 Balance Laws with Linear Excitation362

11.11 An Inhomogeneous Conservation Law365

11.12 Notes370

Ⅻ Genuinely Nonlinear Systems of Two Conservation Laws373

12.1 Notation and Assumptions373

12.2 Entropy-Entropy Flux Pairs and the Hodograph Transformation375

12.3 Local Structure of Solutions378

12.4 Propagation of Riemann Invariants Along Extremal Backward Characteristics381

12.5 Bounds on Solutions398

12.6 Spreading of Rarefaction Waves410

12.7 Regularity of Solutions415

12.8 Initial Data in L1417

12.9 Initial Data with Compact Support421

12.10 Periodic Solutions427

12.11 Notes432

ⅩⅢ The Random Choice Method435

13.1 The Construction Scheme435

13.2 Compactness and Consistency438

13.3 Wave Interactions,Approximate Conservation Laws and Approximate Characteristics in Genuinely Nonlinear Systems444

13.4 The Glimm Functional for Genuinely Nonlinear Systems448

13.5 Bounds on the Total Variation for Genuinely Nonlinear Systems453

13.6 Bounds on the Supremum for Genuinely Nonlinear Systems455

13.7 General Systems457

13.8 Wave Tracing460

13.9 Inhomogeneous Systems of Balance Laws463

13.10 Notes474

ⅩⅣ The Front Tracking Method and Standard Riemann Semigroups477

14.1 Front Tracking for Scalar Conservation Laws478

14.2 Front Tracking for Genuinely Nonlinear Systems of Conservation Laws480

14.3 The Global Wave Pattern485

14.4 Approximate Solutions486

14.5 Bounds on the Total Variation488

14.6 Bounds on the Combined Strength of Pseudoshocks491

14.7 Compactness and Consistency494

14.8 Continuous Dependence on Initial Data496

14.9 The Standard Riemann Semigroup500

14.10 Uniqueness of Solutions501

14.11 Continuous Glimm Functionals,Spreading of Rarefaction Waves,and Structure of Solutions507

14.12 Stability of Strong Waves510

14.13 Notes512

ⅩⅤ Construction of BV Solutions by the Vanishing Viscosity Method517

15.1 The Main Result517

15.2 Road Map to the ProofofTheorem 15.1.1519

15.3 The Effects of Diffusion521

15.4 Decomposition into Viscous Traveling Waves524

15.5 Transversal Wave Interactions528

15.6 Interaction of Waves of the Same Family532

15.7 Energy Estimates536

15.8 Stability Estimates539

15.9 Notes542

ⅩⅥ Compensated Compactness545

16.1 The Young Measure546

16.2 Compensated Compactness and the div-curl Lemma547

16.3 Measure-Valued Solutions for Systems of Conservation Laws and Compensated Compactness548

16.4 Scalar Conservation Laws551

16.5 A Relaxation Scheme for Scalar Conservation Laws553

16.6 Genuinely Nonlinear Systems of Two Conservation Laws556

16.7 The System of Isentropic Elasticity559

16.8 The System of Isentropic Gas Dynamics564

16.9 Notes567

ⅩⅦ Conservation Laws in Two Space Dimensions573

17.1 Self-Similar Solutions for Multidimensional Scalar Conservation Laws573

17.2 Steady Planar Isentropic Gas Flow576

17.3 Self-Similar Planar Irrotational Isentropic Gas Flow580

17.4 Supersonic Isentropic Gas Flow Past a Ramp of Gentle Slope583

17.5 Regular Shock Reflection on a Wall588

17.6 Shock Collision with a Steep Ramp591

17.7 Notes594

Bibliography597

Author Index693

Subject Index703