Hyperbolic Conservation Laws in Continuum Physics
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1. Balance Laws1.1 Formulation of the Balance Law 1.2 Reduction to Field Equations 1.3 Change of Coordinates 1.4 Systems of Balance Laws 1.5 Companion Systems of 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 Banalce Laws 1.10 Notes 2. 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 Notes 3. Hyperbolic Systems of Balance Laws3.1 Hyperbolicity 3.2 Entropy-Entropy Flux Pairs 3.3 Examples of Hyperbolic Systems of Balance Laws 3.4 Notes 4. The Initial-Value Problem: Admissibility of Solutions 4.1 The Initial-Value Problem 4.2 The Burgers Equation and Nonuniqueness of Weak Solutions 4.3 Entropies and Admissible Solutions 4.4 The Vanishing Viscosity Approach 4.5 Initial-Boundary Value Problems 4.6 Notes 5. Entropy and the Stability of Classical Solutions 5.1 Convex Entropy and the Existence of Classical Solutions 5.2 Convex Entropy and the Stability of Classical Solutions 5.3 Partially Convex Entropies and Involutions 5.4 Notes 6. The L1 Theory of Scalar Balance Laws7. Hyperbolic Systems of Balance Laws in One Space Dimension 8. Admissible Shocks 9. Admissible Wave Fans and the Riemann Problem10. Generalized Characteristics11. Genuinely Nonlinear Scalar Conservation Law12. Genuinely Nonlinear Systems of Two Conservation Laws 13. The Random Choice Method 14. The Method of Wave Front Tracking and the Standard Riemann Semigroup15. The Method of Compensated Compactness Bibliography.
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