Mathematics > Analysis of PDEs
[Submitted on 3 Mar 2025
]
Title: Asymptotics of solutions to the porous medium equation near conical singularities
Title: 近锥奇点处多孔介质方程解的渐进行为
Abstract: We show that, on a manifold with conical singularities, the geometry of the cross-section is reflected in the solutions to the porous medium equation near the conic points: We prove that the asymptotics of the solutions near the conical points are determined by the spectrum of the Laplacian on the cross-section. The key to this result is a precise description of the maximal domain of the cone Laplacian.
Submission history
From: Nikolaos Roidos Prof. Dr. [view email][v1] Mon, 3 Mar 2025 20:47:26 UTC (21 KB)
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