本書是第三版，較第二版做了全面修訂，增加了大量應用實例；包括了從1800年-1957年早期歷史的一個全新詳述；並新增一章重述了經典動力學中的開放問題最新解。參考文獻由超過1500篇。內容囊括了存在性、唯一性、連續依賴性、熵解的大量性質、標度守恆律、和普通的雙曲系統等。本書被稱為是研究雙曲守恆律的聖經。Constantine M. Dafermos是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。

Ⅰ Balance Laws1.1 Formulation of the Balance Law1.2 Reduction to Field Equations1.3 Change of Coordinates and a Trace Theorem1.4 Systems of Balance Laws1.5 Companion Balance Laws1.6 Weak and Shock Fronts1.7 Survey of the Theory of BV Functions1.8 BV Solutions of Systems of Balance Laws1.9 Rapid Oscillations and the Stabilizing Effect of Companion Balance Laws1.10 NotesⅡ Introduction to Continuum Physics2.1 Bodies and Motions2.2 Balance Laws in Continuum Physics2.3 The Balance Laws of Continuum Thermomechanics2.4 Material Frame Indifference2.5 Thermoelasticity2.6 Thermoviscoelasticity2.7 Incompressibility2.8 Relaxation2.9 NotesⅢ Hyperbolic Systems of Balance Laws3.1 Hyperbolicity3.2 Entropy-Entropy Flux Pairs3.3 Examples of Hyperbolic Systems of Balance Laws3.4 NotesⅣ The Cauchy Problem4.1 The Cauchy Problem: Classical Solutions4.2 Breakdown of Classical Solutions4.3 The Cauchy Problem: Weak Solutions4.4 Nonuniqueness of Weak Solutions4.5 Entropy Admissibility Condition4.6 The Vanishing Viscosity Approach4.7 Initial-Boundary Value Problems4.8 NotesⅤ Entropy and the Stability of Classical Solutions5.1 Convex Entropy and the Existence of Classical Solutions5.2 The Role of Damping and Relaxation5.3 Convex Entropy and the Stability of Classical Solutions5.4 Involutions5.5 Contingent Entropies and Polyconvexity5.6 Initial-Boundary Value Problems5.7 NotesⅥ The L1 Theory for Scalar Conservation Laws6.1 The Cauchy Problem: Perseverance and Demiseof Classical Solutions6.2 Admissible Weak Solutions and their Stability Properties6.3 The Method of Vanishing Viscosity6.4 Solutions as Trajectories of a Contraction Semigroup6.5 The Layering Method6.6 Relaxation6.7 A Kinetic Formulation6.8 Fine Structure of L1 Solutions6.9 Initial-Boundary Value Problems6.10 The Lt Theory for Systems of Conservation Laws6.11 NotesⅦ Hyperbolic Systems of Balance Laws in One-Space Dimension7.1 Balance Laws in One-Space Dimension7.2 Hyperbolicity and Strict Hyperbolicity7.3 Riemann Invariants7.4 Entropy-Entropy Flux Pairs7.5 Genuine Nonlinearity and Linear Degeneracy7.6 Simple Waves7.7 Explosion of Weak Fronts7.8 Existence and Breakdown of Classical Solutions7.9 Weak Solutions7.10 NotesⅧ Admissible Shocks8.1 Strong Shocks, Weak Shocks, and Shocks of Moderate Strength8.2 The Hugoniot Locus8.3 The Lax Shock Admissibility Criterion； Compressive, Overcompressive and Undercompressive Shocks.8.4 The Liu Shock Admissibility Criterion8.5 The Entropy Shock Admissibility Criterion8.6 Viscous Shock Profiles8.7 Nonconservative Shocks8.8 NotesⅨ Admissible Wave Fans and the Riemann Problem9.1 Self-Similar Solutions and the Riemann Problem9.2 Wave Fan Admissibility Criteria9.3 Solution of the Riemann Problem via Wave Curves9.4 Systems with Genuinely Nonlinear or Linearly Degenerate Characteristic Families9.5 General Strictly Hyperbolic Systems9.6 Failure of Existence or Uniqueness； Delta Shocks and Transitional Waves9.7 The Entropy Rate Admissibility Criterion9.8 Viscous Wave Fans9.9 Interaction of Wave Fans9.10 Breakdown of Weak Solutions9.11 NotesⅩ Generalized Characteristics10.1 BV Solutions10.2 Generalized Characteristics10.3 Extremal Backward Characteristics10.4 NotesⅪ Genuinely Nonlinear Scalar Conservation Laws11.1 Admissible BV Solutions and Generalized Characteristics11.2 The Spreading of Rarefaction Waves11.3 Regularity of Solutions11.4 Divides, Invariants and the Lax Formula11.5 Decay of Solutions Induced by Entropy DissipationI 1.6 Spreading of Characteristics and Development of N-Waves11.7 Confinement of Characteristics and Formation of Saw-toothed Profiles11.8 Comparison Theorems and L1 Stability11.9 Genuinely Nonlinear Scalar Balance Laws11.10 Balance Laws with Linear Excitation11. 11 An Inhomogeneous Conservation Law11.12 Notes……Ⅻ Genuinely Nonlinear Systems of Two Conservation LawsⅩⅢ The Random Choice MethodⅩⅣ The Front Tracking Method and Standard Riemann SemigroupsⅩⅤ Construction of BV Solutions by the Vanishing Viscosity Method.ⅩⅥ Compensated CompactnessⅩⅦ Conservation Laws in Two Space Dimensions