LOCAL SOLVABILITY OF AN INITIAL BOUNDARY VALUE PROBLEM FOR A QUASILINEAR HYPERBOLIC-PARABOLIC SYSTEM

Abstract

This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in Hs, where s is an integer satisfying s ≥ [n/2]+1.