CONVERGENCE RATES TO NONLINEAR DIFFUSIVE WAVES FOR SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEM

This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of classical solutions is proven,and L~p convergence rates are obtained. Compared with the results obtained by Hsiao and Liu, better convergence rates are obtained in this article.     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.