Weak asymptotic solution for a non-strictly hyperbolic system of conservation laws

Abstract

In this article, we construct the weak asymptotic solution developed by Panov and Shelkovich for piecewise known solutions to a prolonged system of conservation laws. This is done by introducing four singular waves along a discontinuity curve, which in turn implies the existence of weak asymptotic solutions for the Riemann type initial data. By piecing together the Riemann problems, we construct weak asymptotic solution for general type initial data. © 2015 Texas State University - San Marcos.