Method for symmetrization and estimation of solutions of the Neumann problem for the equation of a porous medium in domains with noncompact boundary for infinitely increasing time

Abstract

We consider the initial boundary-value Neumann problem for the equation of a porous medium in a domain with noncompact boundary. By using a symmetrization method, we obtain exactL _p-estimates, 1≤p≤∞, for solutions as t→∞.