Delta-Wave in a Simple 1-D 2x2 Hyperbolic Problem

Abstract

A simple one-dimensional $2\times 2$ hyperbolic system is considered in the paper. The model contains a linear hyperbolic equation, as well as a hyperbolic equation of which the coefficients are about the solution of the linear one. The exact solution is presented and discussed, then numerical experiments are given by TVD (or MmB) type schemes for Riemann problems. From the results, we know that the solutions do have $\delta-$waves for some suitable initial data.