CONSTRUCTION AND QUALITATIVE BEHAVIOR OF SOLUTIONS FOR A SYSTEM OF NONLINEAR HYPERBOLIC CONSERVATION-LAWS WITH DAMPING

The paper considers hyperbolic conservation laws with damping. This system may be viewed as isentropic Euler equations in Lagrangian coordinates. The well-known porous media equation can be obtained by approximating the second equation with Darcy's law. It is proved that Darcy's law can be obtained, in fact, from a more complete equation time-asymptotically. Nonlinear diffusive phenomena in the solutions of these equations are discovered where the diffusion effect created by the damping is studied for a solution without shock waves. (from Authors)