Asymptotics of solutions to the porous medium equation near conical singularities

2025/03/03 by Nikolaos Roidos, Roidos, Nikolaos, Elmar Schrohe +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2503.02044

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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• Evolution Equations on Manifolds with Conical Singularities

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