The incompressible limit of an inhomogeneous model of tissue growth

2025/03/25 by Sulak, Anthony, Turanova, Olga · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.19849

Abstract

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 L⁴ bound on the gradient of the pressure and an estimate of Aronson-Bénilan type.

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• A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization

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