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arXiv · 0902.1869

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

Valérie Le Blanc
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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 Kružkov type entropy. And when the space dimension is one, we estimate the number of sign changes of a solution to obtain $L^1$-stability.

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Valérie Le Blanc. 2009-02-11. $L^1$-stability of periodic stationary solutions of scalar convection-diffusion equations. https://arxiv.org/abs/0902.1869

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