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arXiv · 1810.12239

On the long time behavior of a tumor growth model

Alain Miranville·Elisabetta Rocca·Giulio Schimperna
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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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Alain Miranville, Elisabetta Rocca, Giulio Schimperna. 2018-10-29. On the long time behavior of a tumor growth model. https://arxiv.org/abs/1810.12239

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