Weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation

Abstract

In this paper, we explore the weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation which describes strictly hyperbolic quasilinear system of conservation laws. For the Riemann problem, we provide a global existence and uniqueness result of exact solution. Further, we establish the exact solution explicitly in terms of one parameter family of elementary wave curves. We devise a necessary and sufficient condition on initial data for which the solution of the Riemann problem consists of either a shock wave or a simple wave according to one and three family of characteristic curves. Lastly, we analyze the Von Neumann result related to collision of weak shock waves of same family.