The asymptotic behaviour of solutions to initial value problems for a nonlinear system of conservation laws with discontinuous initial data

This paper is concerned with the asymptotic behaviour of solutions to initial value problems for a nonlinear system of conservation laws with discontinuous initial data.LetΓ_1 be a polygonal line formed by two rays,andΓ_2 be a curve coincide with except a finite part.The author studied Riemann problems of the given system with their initial data having discontinuity on and respectively.The solutions to these two Riemann problems are constructed.It is found that the former solution is a selfsimilar solution,while the latter is not.The main conclusion in this paper is that the latter approaches the former in macroscope sense when t tends to infinity.