Quasilinear hyperbolic systems and dissipative mechanisms
The talk is given to introduce recent developments on the subject of quasilinear hyperbolic systems with dissipation,particularly the systems of hyperpolic conservation laws with either lower order dissipation such as frictional damping and relaxation, or higher order dissipation such as viscosity and heat diffution. The emphasis is, on the one hand to the damping mechanism or higher order dissipation, to understand the influence of dissipation on the qualitative behavior of solutions, such as the nonlinear diffusive phenomena, phase transitions, etc., and on the other hand to relaxation effects, to employ dissipation as a device for approximating solutions of hyperbolic systems by passing to the zero relaxation limit.
Hsiao Ling, Academia Sinica, China
October 22, 1999