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

Valérie Le Blanc (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: lap number; $L^1$-stability; periodic stationary solutions; entropy; dispersion inequality; lap number.

Domaines: Equations aux dérivées partielles [math.AP]

Valérie Le Blanc. $L^1$-stability of periodic stationary solutions of scalar convection-diffusion equations. 2009. ⟨hal-00360402⟩