Answers are grounded in this paper and cite their sources.
Analysis reveals the asymptotic behavior of solutions in manifolds with conical singularities, suggesting geometric implications.
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.
No takes yet. Share an insight, caveat, or question.
Roidos et al. (2025) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: