An L1 bound for |ux (t,x) | in a one-dimensional parabolic conservation system

Abstract

This paper reports an L1 bound for |uxt,x | in a one dimensional parabolic system of conservation laws that is used elsewhere 3,4 when establishing global existence and optimal decay estimates by means of entropy flux pairs for the system where u = u1,...,un T and f u = f1u,...,fnu T are n ×1 column vectors, with f u a smooth function defined in a ball of radius r centered at a fixed vector ūε Rn, and ε >0 is a constant.