On the long time behavior of a tumor growth model

2018/10/29 by Miranville, Alain, Rocca, Elisabetta, Schimperna, Giulio · 1 citation
#35B41 #35D30 #35K57 #35Q92 #37L30 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.12239

Abstract

We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type equation for the tumor phase coupled with a reaction-diffusion equation for the nutrient concentration. We prove that, under physically motivated assumptions on parameters and data, the corresponding initial-boundary value problem generates a dissipative dynamical system that admits the global attractor in a proper phase space.

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• An Allen-Cahn tumor growth model with temperature

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