Decay of solutions to anisotropic conservation laws with large initial data

Abstract

In this paper, we study the large time behavior of solutions to the Cauchy problem for the anisotropic conservation laws in two dimensional space. Without any smallness assumption on the initial data, the decay rates of solutions in $L^2$ space and homogeneous Sobolev space ${\dot{H}}^{\gamma }$ are obtained by using the method of time-frequency decomposition and the classical energy method.