Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities

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.