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

We examine the Cauchy problem for a nonlinear dissipative evolution system with conservation form with initial condition where α, β, σ and ν are positive constants such that α < σ and β < 1. We establish the global existence and decay rate of the solution subject to the parameter restriction . The optimal decay rate is obtained if (ψ0, θ0) ∈ 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 (ψ0, θ0) ∈ H1(R, R2)∩L 1(R, R2).