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arXiv · 2503.02044

Asymptotics of solutions to the porous medium equation near conical singularities

Nikolaos Roidos·Elmar Schrohe
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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.

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Nikolaos Roidos, Elmar Schrohe. 2025-03-03. Asymptotics of solutions to the porous medium equation near conical singularities. https://arxiv.org/abs/2503.02044

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