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arXiv · 2503.19849

The incompressible limit of an inhomogeneous model of tissue growth

Anthony Sulak·Olga Turanova
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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 $L^4$ bound on the gradient of the pressure and an estimate of Aronson-B\'{e}nilan type.

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Anthony Sulak, Olga Turanova. 2025-03-25. The incompressible limit of an inhomogeneous model of tissue growth. https://arxiv.org/abs/2503.19849

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