Well-posedness of the global entropy solution to the Cauchy problem of a hyperbolic conservation laws with relaxation

In this paper, we prove that the Cauchy problem to a hyperbolic conservation laws with relaxation with singular initial data admits a unique global entropy solution in the sense of Definition 1.1. Compared with former results in this direction, the main ingredient of this paper lies in the fact that it contains a uniqueness result and we do not ask f (u) to satisfy any convex, monotonic conditions and the regularity assumption we imposed on f (u) is weaker.  2003 Elsevier Inc. All rights reserved