Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass

Fuente: arXiv
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Main Author: Dembski, Kevin H.
Format: Preprint
Published: 2025
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author Dembski, Kevin H.
author_facet Dembski, Kevin H.
contents We prove finite-time singularity formation for Lipschitz continuous solutions of the inviscid porous medium equation which vanish on the boundary of the domain. As the density vanishes on the boundary of the domain, the full regularizing effect of transport is present and must be overcome. The solutions are smooth away from the origin and the density can be made compactly supported.
format Preprint
id arxiv_https___arxiv_org_abs_2511_01827
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass
Dembski, Kevin H.
Analysis of PDEs
We prove finite-time singularity formation for Lipschitz continuous solutions of the inviscid porous medium equation which vanish on the boundary of the domain. As the density vanishes on the boundary of the domain, the full regularizing effect of transport is present and must be overcome. The solutions are smooth away from the origin and the density can be made compactly supported.
title Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass
topic Analysis of PDEs
url https://arxiv.org/abs/2511.01827