Generalized shadow waves solution to a system of Riemann type initial data

Abstract

In this paper, we study a system of a non-strictly hyperbolic of conservation laws when viscosity is present. We do not use classical solution. We construct a shadow wave solution (see [9]) for Riemann type initial data where the first component develops rarefaction, which was partially determined in [5] using vanishing viscosity method. For shadow wave approach, we used only convex entropy and its corresponding entropy.