$L^1$-stability of periodic stationary solutions of scalar convection-diffusion equations

Abstract

The aim of this paper is to study the $L^1$-stability of periodic stationary solutions of scalar convection-diffusion equations. We obtain dispersion in $L^2$ for all space dimensions using Kru\v{z}kov type entropy. And when the space dimension is one, we estimate the number of sign changes of a solution to obtain $L^1$-stability.