ESTIMATE OF THE TIME RATE OF ENTROPY DISSIPATION FOR SYSTEMS OF CONSERVATION-LAWS

A priori estimates for weak solutions of nonlinear systems of conserva tion laws remain in short supply. In this note we obtain an estimate o f the rate of total entropy dissipation for initial/boundary value pro blems for such systems, of any dimension and in any number of space va riables. The essential assumptions made are those of a strictly convex entropy density, an L(infinity) estimate on the solution, and initial data of ''bounded variation'' as described here. (C) 1996 Academic Pr ess, Inc.