Chapter 1. Fundamental concepts and exaniples
1. Hyperbolicity, genume nonlinearity, and entropies
2. Shock formation and weak solutions
3. Singular limits and the entropy inequality
4. Examples of diffusive-dispersive models
5. Kinetic relations and traveling waves
Part 1. SCALAR CONSERVATION LAWS
Chapter II. The Riemann problem
1. Entropy conditions
2. Classical Riemann solver
3. Entropy dissipation function
4. Nonclassical Riemann solver for concave-convex flux
5. Nonclassical Riemann solver for convex-concave flux
Chapter III. Diffusive-dispersive traveling waves
1. Diffusive traveling waves
2. Kinetic functions for the cubic flux
3. Kinetic functions for general flux
4. Traveling waves for a given speed
5. Traveling waves for a given diffusion-dispersion ratio
Chapter IV. Existence theory for the Cauchy problem
1. Classical entropy solutions for convex flux
2. Classical entropy solutions for general flux
3. Nonclassical entropy solutions
4. Refined estimates
Chapter V. Continuous dependence of solutions
1. A class of linear hyperbolic equations
2. L^1 continuous dependence estimate
3. Sharp version of the continuous dependence estimate
4. Generalizations
Part 2. SYSTEMS OF CONSERVATION LAWS
Chapter VI. The Riemann problem
1. Shock and rarefaction waves
2. Classical Riemann solver
3. Entropy dissipation and wave sets
4. Kinetic relation and nonclassical Riemann solver
Chapter VII. Classical entropy solutions of the Cauchy problem
1. Glimm interaction estimates
2. Existence theory
3. Uniform estimates
4. Pointwise regularity properties
Chapter VIII. Nonclassical entropy solutions of the Cauchy problem
1. A generalized total variation functional
2. A generalized weighted interaction potential
3. Existence theory
4. Pointwise regularity properties
Chapter IX. Continuous dependence of solutions
1. A class of linear hyperbolic systems
2. L^1 continuous dependence estimate
3. Sharp version of the continuous dependence estimate
4. Generalizations
Chapter X. Uniqueness of entropy solutions
1. Admissible entropy solutions
2. Tangency property
3. Uniqueness theory
4. Applications
Appendix. Functions with bounded variation
Bibliographical notes
References