Stability and decay rate of space-periodic solutions to porous medium equations with convection

Abstract

In this paper, we discuss the asymptotic stability of periodic solutions in the spacial variable to porous medium equations with convection. At first, based on the argument method of the ω-limit set theory in ordinary differential equations, we obtain that the periodic solution with a periodic initial function exponentially decays to its average. Then, using this result, the anti-derivative technique and energy estimates, we prove the asymptotic stability of the periodic solution and give a time decay rate.