Critical asymptotic behaviour for a perturbed conservation law

Article type: Research Article

Authors: Reyes, G.

Affiliations: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P. le A. Moro 5, I‐00185 Roma, Italia E‐mail: reyes@mat.uniroma1.it

Abstract: In this paper we study the intermediate asymptotics as t→∞ of nontrivial, nonnegative solutions to the Cauchy problem for the following nonlinear first order equation: ut+(um)x+up=0, with m>1, p=m+1. We prove that for any bounded, nonnegative, compactly supported initial data the asymptotic behaviour is given in first approximation by a universal function W, which is a contracted “N‐wave” with logarithmically decaying mass.

Journal: Asymptotic Analysis, vol. 25, no. 2, pp. 109-122, 2001