Multidimensional hyperbolic partial differential equations : first-order systems and applications

Preface Introduction Notations THE LINEAR CAUCHY PROBLEM 1. Linear Cauchy problem with constant coefficients 2. Linear Cauchy problem with variable coefficients THE LINEAR INITIAL BOUNDARY VALUE PROBLEM 3. Friedrichs symmetric dissipative IBVPs 4. Initial boundary value problem in a half-space with constant coefficients 5. Construction of a symmetrizer under (UKL) 6. The characteristic IBVP 7. The homogeneous IBVP 8. A classification of linear IBVPs 9. Variable coefficients initial boundary value problems NONLINEAR PROBLEMS 10. The Cauchy problem for quasilinear systems 11. The mixed problem for quasilinear systems 12. Persistence of multidimensional shocks APPLICATIONS TO GAS DYNAMICS 13. The Euler equations for real fluids 14. Boundary conditions for Euler equations 15. Shock stability in gas dynamics APPENDIX A. Basic calculus results B. Fourier and Laplace analysis C. Pseudo/para-differential calculus Bibliography Index