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.

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

“…Ambika and Radha [36] analyzed the interaction of two weak shocks of the Riemann problem for gas dynamic equations and noticed that the interaction leads to simple wave and shock wave depending on the adiabatic constant. The existence and uniqueness and interactions of weak shock waves of the Riemann solution for drift-flux compressible two-phase flow model and isentropic flux perturbed Cargo-LeRoux model have been explored by Kuila et al [37,38]. Shao [39] investigated whether the Riemann solutions for linearly degenerate hyperbolic conservation laws preserve their global structural stability after minor BV perturbations of the initial data.…”