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Bibliographic Details
Main Authors: Sulak, Anthony, Turanova, Olga
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.19849
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author Sulak, Anthony
Turanova, Olga
author_facet Sulak, Anthony
Turanova, Olga
contents We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an $L^4$ bound on the gradient of the pressure and an estimate of Aronson-Bénilan type.
format Preprint
id arxiv_https___arxiv_org_abs_2503_19849
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The incompressible limit of an inhomogeneous model of tissue growth
Sulak, Anthony
Turanova, Olga
Analysis of PDEs
We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an $L^4$ bound on the gradient of the pressure and an estimate of Aronson-Bénilan type.
title The incompressible limit of an inhomogeneous model of tissue growth
topic Analysis of PDEs
url https://arxiv.org/abs/2503.19849