On convergence to entropy solutions of a single conservation law

Abstract

Estimates of the difference between the entropy solutions of the single conservation law ut+div g(u) = 0, u(0, ·) = u0 and of the evolutionary integral equation (k * (u-u0))t+div g(u) = 0 are given in terms of k, g and u0. A corresponding result is obtained for more general evolution equations with an accretive non-linearity. © 1996 Academic Press, Inc.