On the long time behavior of a tumor growth model

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 equ...

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Bibliographic Details
Published in:Journal of Differential Equations 2019-08, Vol.267 (4), p.2616-2642
Main Authors: Miranville, Alain, Rocca, Elisabetta, Schimperna, Giulio
Format: Article
Language:English
Subjects:
Dissipativity
Global attractor
Initial-boundary value problem
Phase field model
Tumor growth
Well-posedness
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.03.028