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

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

2009-02-11

arxiv.org/abs/0902.1869v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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