THE ASYMPTOTIC-BEHAVIOR OF THE HYPERBOLIC CONSERVATION-LAWS WITH RELAXATION ON THE QUARTER-PLANE

The hyperbolic conservation laws with relaxation appear in many physic al models such as those for gas dynamics with thermo-nonequilibrium, e lasticity with memory, flood flow with friction, and traffic flow. The main concern of this article is the long-time behavior of the interac tion between the relaxations and the boundary conditions. In this arti cle, we investigate this problem for a simple model of a 2x2 system. I t is proven that the solution of the system asymptotically converges t o a traveling wave moving away from the boundary under suitable condit ions on the boundary.