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arXiv · 2102.03844

Existence and incompressible limit of a tissue growth model with autophagy

Jian-Guo Liu·Xiangsheng Xu
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Abstract

In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate the limiting behavior of solutions as the pressure gets stiff. The so-called incompressible limit is a free boundary problem of Hele-Shaw type. Our key new discovery is that the usual energy estimate still holds as long as the time variable stays away from $0$.

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Jian-Guo Liu, Xiangsheng Xu. 2021-02-07. Existence and incompressible limit of a tissue growth model with autophagy. https://arxiv.org/abs/2102.03844

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