Large time profile of solutions for a dissipative nonlinear evolution system with conservational form

Abstract

We examine the Cauchy problem for a nonlinear dissipative evolution system with conservation form with initial condition where ?, ?, ? and ? are positive constants such that ? < ? and ? < 1. We establish the global existence and decay rate of the solution subject to the parameter restriction . The optimal decay rate is obtained if (?0, ?0) L1(R, R2) furthermore. The global existence of the solution to the same problem has been studied in Jian and Chen (1998 Acta Math. Sin. 14 17?34) without giving the decay rate and optimal decay order of the solution, in which (?0, ?0) H1(R, R2)?L1(R, R2).