The Initial Boundary Value Problems for Hyperbolic Conservation Laws with Relaxation

The hyperbolic conservation laws with relaxation appear in many physical models such as those for gas dynamics with thermo-non-equilibrium, elasticity with memory, flood flow with friction, traffic flow, etc.. The main concern of this article is the long-time effect of the relaxations on the boundary layer behaviors. In this article, we investigate this problem for a simple model of 2×2 systems. Conditions relating the boundary data and far field states are found for the existence of the boundary layers. Also, it is proven that the boundary layers thus obtained are nonlinearly stable.