Existence and Incompressible Limit of a Tissue Growth Model with Autophagy

DOI10.1137/21M1405253zbMath1473.35079arXiv2102.03844OpenAlexW3199708239MaRDI QIDQ3383046

Xiangsheng Xu, Jian-Guo Liu

Publication date: 23 September 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.03844

zbMATH Keywords

cross-diffusion systemnon-symmetric and degenerate coefficient matrix

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Free boundary problems for PDEs (35R35) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

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Existence of Solutions to Reaction Cross Diffusion Systems ⋮ Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit ⋮ Convergence rate for the incompressible limit of nonlinear diffusion-advection equations ⋮ Incompressible limits of the Patlak-Keller-Segel model and its stationary state ⋮ A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model ⋮ On the incompressible limit for a tumour growth model incorporating convective effects ⋮ A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit

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