Existence and maximal $L^{p}$-regularity of solutions for the porous medium equation on manifolds with conical singularities

Nikolaos Roidos, Elmar Schrohe

Published 2015-04-20Version 1

We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness and maximal $L^{p}$-regularity of a short time solution. In particular, we obtain information on the short time asymptotics of the solution near the conical point. Our method is based on bounded imaginary powers results for cone differential operators on Mellin-Sobolev spaces and $R$-sectoriality perturbation techniques.