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

In this article we introduce a concept of entropy weak asymptotic solution for a system of conservation laws and construct the same for a prolonged system of conservation laws which is highly non-strictly hyperbolic. This is first done for Riemann type initial data by introducing $\delta,\delta',\delta''$ waves along a discontinuity curve and then for general initial data by piecing together the Riemann solutions.