Estimate of the time rate of entropy dissipation for systems of conservation laws

A priori estimates for weak solutions of nonlinear systems of conservation laws remain in short supply. In this note we obtain an estimate of the rate of total entropy dissipation for initial/boundary value problems for such systems, of any dimension and in any number of space variables. The essential assumptions made are those of a strictly convex entropy density, an L_∞ estimate on the solution, and initial data of "bounded variation" as described here.