Preface
Contents
Chapter Ⅰ Ordinary differential equations
1.1 Introduction
1.2 Local existence and uniqueness for the Cauchy problem
1.3 Existence of solutions in the large
1.4 Generalized solutions
Chapter Ⅱ Scalar first order equations with one space variable
2.1 Introduction
2.2 The linear case
2.3 Classical solutions of Burgesequation
2.4 Weak solutions of Burgersequation
2.5 General strictly convex conservation laws
Chapter Ⅲ Scalar first order equations with several variables
3.1 Introduction
3.2 Parabolic equations
3.3 The conservation law with viscosity
3.4 The entropy solution of the conservation law
Chapter Ⅳ First order systems of conservation laws with one space variable
4.1 Introduction
4.2 Generalities on first order systems
4.3 The lifespan of classical solutions
4.4 The Riemann problem
4.5 Glimms existence theorem
4.6 Entropy pairs
Chapter Ⅴ Compensated compactness
5.1 Introduction
5.2 Weak convergence in Loo
5.3 Weak convergence of solutions of linear differential equations
5.5 Probability measures associated with a system of two equetions
5.6 Existence of weak solutions for a system of two equations
Chapter Ⅵ Nonlinear perturbations of the wave equation
Chapter Ⅶ Nonlinear perturbations of the Klein-Gordon equation
Chapter Ⅷ Microlocal analysis
Chapter Ⅸ Pseudo-differential operators of type1，1
Chapter Ⅹ Paradifferential calculus
Chapter Ⅺ Propagation of singularities
Appendix on pseudo-Riemannian geometry
References
Index of notation
Index
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