IUMJ

Title: Invariance property of a conservation law without convexity

Authors: Mijoung Kim and Yong-Jung Kim

Issue: Volume 58 (2009), Issue 2, 733-750

Abstract:

The main goal of this paper is to investigate the mechanism of a conservation law that gives the $N$-wave like asymptotics. It turns out that the positivity of the flux function provides a certain invariance of solution which singles out the right asymptotics among two parameter family of $N$-waves. Two kinds of long time asymptotic convergence orders in $L^1$-norm to this $N$-wave are proved using a potential comparison technique. The first one is of the magnitude of the $N$-wave itself and the second one is of order $1/t$. We observe that these asymptotic convergence orders are related to space and time translations of potentials.