达夫莫斯编著的《连续介质物理中的双曲守恒律(第3版)(英文版)》是第三版，较第二版做了全面修订，增加了大量应用实例；包括了从1800年-1957年早期历史的一个全新详述；并新增一章重述了经典动力学中的开放问题最新解。参考文献由超过1500篇。内容囊括了存在性、唯一性、连续依赖性、熵解的大量性质、标度守恒律、和普通的双曲系统等。本书被称为是研究双曲守恒律的圣经。

Ⅰ Balance Laws

 1.1 Formulation of the Balance Law

 1.2 Reduction to Field Equations

 1.3 Change of Coordinates and a Trace Theorem

 1.4 Systems of Balance Laws

 1.5 Companion Balance Laws

 1.6 Weak and Shock Fronts

 1.7 Survey of the Theory of BV Functions

 1.8 BV Solutions of Systems of Balance Laws

 1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws

 1.10 Notes

Ⅱ Introduction to Continuum Physics

 2.1 Bodies and Motions

 2.2 Balance Laws in Continuum Physics

 2.3 The Balance Laws of Continuum Thermomechanics

 2.4 Material Frame Indifference

 2.5 Thermoelasticity

 2.6 Thermoviscoelasticity

 2.7 Incompressibility

 2.8 Relaxation

 2.9 Notes

Ⅲ Hyperbolic Systems of Balance Laws

 3.1 Hyperbolicity

 3.2 Entropy-Entropy Flux Pairs

 3.3 Examples of Hyperbolic Systems of Balance Laws

 3.4 Notes

Ⅳ The Cauchy Problem

 4.1 The Cauchy Problem: Classical Solutions

 4.2 Breakdown of Classical Solutions

 4.3 The Cauchy Problem: Weak Solutions

 4.4 Nonuniqueness of Weak Solutions

 4.5 Entropy Admissibility Condition

 4.6 The Vanishing Viscosity Approach

 4.7 Initial-Boundary Value Problems

 4.8 Notes

Ⅴ Entropy and the Stability of Classical Solutions

 5.1 Convex Entropy and the Existence of Classical Solutions

 5.2 The Role of Damping and Relaxation

 5.3 Convex Entropy and the Stability of Classical Solutions

 5.4 Involutions

 5.5 Contingent Entropies and Polyconvexity

 5.6 Initial-Boundary Value Problems

 5.7 Notes

Ⅵ The L1 Theory for Scalar Conservation Laws

 6.1 The Cauchy Problem: Perseverance and Demise

 of Classical Solutions

 6.2 Admissible Weak Solutions and their Stability Properties

 6.3 The Method of Vanishing Viscosity

 6.4 Solutions as Trajectories of a Contraction Semigroup

 6.5 The Layering Method

 6.6 Relaxation

 6.7 A Kinetic Formulation

 6.8 Fine Structure of L1 Solutions

 6.9 Initial-Boundary Value Problems

 6.10 The Lt Theory for Systems of Conservation Laws

 6.11 Notes

Ⅶ Hyperbolic Systems of Balance Laws in One-Space Dimension

 7.1 Balance Laws in One-Space Dimension

 7.2 Hyperbolicity and Strict Hyperbolicity

 7.3 Riemann Invariants

 7.4 Entropy-Entropy Flux Pairs

 7.5 Genuine Nonlinearity and Linear Degeneracy

 7.6 Simple Waves

 7.7 Explosion of Weak Fronts

 7.8 Existence and Breakdown of Classical Solutions

 7.9 Weak Solutions

 7.10 Notes

Ⅷ Admissible Shocks

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

 8.2 The Hugoniot Locus

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

 8.4 The Liu Shock Admissibility Criterion

 8.5 The Entropy Shock Admissibility Criterion

 8.6 Viscous Shock Profiles

 8.7 Nonconservative Shocks

 8.8 Notes

Ⅸ Admissible Wave Fans and the Riemann Problem

 9.1 Self-Similar Solutions and the Riemann Problem

 9.2 Wave Fan Admissibility Criteria

 9.3 Solution of the Riemann Problem via Wave Curves

 9.4 Systems with Genuinely Nonlinear or Linearly Degenerate Characteristic Families

 9.5 General Strictly Hyperbolic Systems

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

 9.7 The Entropy Rate Admissibility Criterion

 9.8 Viscous Wave Fans

 9.9 Interaction of Wave Fans

 9.10 Breakdown of Weak Solutions

 9.11 Notes

Ⅹ Generalized Characteristics

 10.1 BV Solutions

 10.2 Generalized Characteristics

 10.3 Extremal Backward Characteristics

 10.4 Notes

Ⅺ Genuinely Nonlinear Scalar Conservation Laws

 11.1 Admissible BV Solutions and Generalized Characteristics

 11.2 The Spreading of Rarefaction Waves

 11.3 Regularity of Solutions

 11.4 Divides, Invariants and the Lax Formula

 11.5 Decay of Solutions Induced by Entropy Dissipation

 11.6 Spreading of Characteristics and Development of N-Waves

 11.7 Confinement of Characteristics and Formation of Saw-toothed Profiles

 11.8 Comparison Theorems and L1 Stability

 11.9 Genuinely Nonlinear Scalar Balance Laws

 11.10 Balance Laws with Linear Excitation

 11.11 An Inhomogeneous Conservation Law

 11.12 Notes

XII Genuinely Nonlinear Systems of Two Conservation Laws

 12.1 Notation and Assumptions

 12.2 Entropy-Entropy Flux Pairs and the Hodograph Transformation

 12.3 Local Structure of Solutions

 12.4 Propagation of Riemann Invariants

 Along Extremal Backward Characteristics

 12.5 Boundson Solutions

 12.6 Spreading of Rarefaction Waves

 12.7 Regularity of Solutions

 12.8 Initial Datain LI

 12.9 Initial Data with Compact Support

 12.10 Periodic Solutions

 12.11 Notes

XIII The Random Choice Method

 13.1 The Construction Scheme

 13.2 Compactness and Consistency

 13.3 Wave Interactions, Approximate Conservation Laws

 and Approximate Characteristics

 in Genuinely Nonlinear Systems

 13.4 The Glimm Functional for Genuinely Nonlinear Systems

 13.5 Bounds on the Total Variation

 for Genuinely Nonlinear Systems

 13.6 Bounds on the Supremum for Genuinely Nonlinear Systems ...

 13.7 General Systems

 13.8 Wave Tracing

 13.9 lnhomogeneous Systems of Balance Laws

 13.10 Notes

XIV The Front Tracking Method and Standard Riemann Semigroups..

 14.1 Front Tracking for Scalar Conservation Laws

 14.2 Front Tracking for Genuinely Nonlinear

 Systems of Conservation Laws

 14.3 The Global Wave Pattern

 14.4 Approximate Solutions

 14.5 Bounds on the Total Variation

 14.6 Bounds on the Combined Strength of Pseudoshocks

 14.7 Compactness and Consistency

 14.8 Continuous Dependence on Initial Data

 14.9 The Standard Riemann Semigroup

 14.10 Uniqueness of Solutions

 14.11 Continuous Glimm Functionals,

 Spreading of Rarefaction Waves,

 and Structure of Solutions

 14.12 Stability of Strong Waves

 14.13 Notes

XV Construction of BV Solutions by the Vanishing Viscosity Method

 15.1 The Main Result

 15.2 Road Map to the Proof of Theorem 15.1.1

 15.3 The Effects of Diffusion

 15.4 Decomposition into Viscous Traveling Waves

 15.5 Transversal Wave Interactions

 15.6 Interaction of Waves of the Same Family

 15.7 Energy Estimates

 15.8 Stability Estimates

 15.9 Notes

XVI Compensated Compactness

 16.1 The Young Measure

 16.2 Compensated Compactness and the div-curl Lemma

 16.3 Measure-Valued Solutions for Systems of Conservation Laws

 and Compensated Compactness

 16.4 Scalar Conservation Laws

 16.5 A Relaxation Scheme for Scalar Conservation Laws

 16.6 Genuinely Nonlinear Systems of Two Conservation Laws ...

 16.7 The System of Isentropic Elasticity

 16.8 The System of Isentropic Gas Dynamics

 16.9 Notes

XVII Conservation Laws in Two Space Dimensions

 17.1 Self-Similar Solutions for Multidimensional Scalar

 Conservation Laws

 17.2 Steady Planar Isentropic Gas Flow

 17.3 Self-Similar Planar Irrotational Isentropic Gas Flow

 17.4 Supersonic Isentropic Gas Flow Past a Ramp of Gentle Slope

 17.5 Regular Shock Reflection on a Wall

 17.6 Shock Collision with a Steep Ramp

 17.7 Notes

Bibliography

Author Index

Subject Index