Asymptotics of solutions to the porous medium equation near conical singularities

Abstract

We show that, on a manifold with conical singularities, the asymptotics of the solutions to the porous medium equation near the conical points are determined by the spectrum of the Laplacian on the cross-section of the cone. The key to this result is a precise description of the maximal domain of the cone Laplacian.

24 pages