Various dissipative mechanisms: viscosity, relaxation, coupling with elliptic equations, BGK models, ... Dissipative limit vs time asymptotics. Dissipation and entropy. A priori estimate. Linear theory: Well-posedness for the Cauchy problem, time asymptotics, relaxation limit. Kawashima's condition ; link with control theory. Various instances of the sub-characteristic property. Discontinuities. How shocks are approached in dissipative structures: shock profiles. Can discontinuities happen in dissipative structures? Nonlinear setting. Entropy formalism. Characteristic fields in hyperbolic-parabolic or hyperbolic-elliptic systems. Nonlinear diffusion waves, asymptotic decay. The scalar case; L^1 stability of travelling waves. Lecture notes (accessible only from SISSA intranet)
Course: Dissipative mechanisms in systems of conservation laws
Research Group:
Speaker:
Denis Serre
Institution:
UMPA Ecole Normale Superieure de Lyon
Schedule:
Thursday, January 12, 2006 - 06:30 to 07:30
Location:
SISSA - Main Building - ground floor - room B
Abstract: