Potential comparison and asymptotics in scalar conservation laws without convexity

Abstract

Two kinds of optimal convergence orders in L-1-norm to a self-similar solution are proved or conjectured for various evolutionary problems so far. The first convergence order is of the magnitude of the similarity solution itself and the second one is of order 1/t. Employing a potential comparison technique to scalar conservation laws we may easily see that these asymptotic convergence orders are related to space and time translation of potentials. We present the technique clearly in the simple setting of scalar conservation laws in one space dimension. (C) 2006 Published by Elsevier Inc.