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arXiv · 2512.15426

On a relaxed Cahn-Hilliard tumour growth model with single-well potential and degenerate mobility

Cecilia Cavaterra·Matteo Fornoni·Maurizio Grasselli·Benoît Perthame
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Abstract

We consider a phase-field system modelling solid tumour growth. This system consists of a Cahn-Hilliard equation coupled with a nutrient equation. The former is characterised by a degenerate mobility and a singular potential. Both equations are subject to suitable reaction terms which model proliferation and nutrient consumption. Chemotactic effects are also taken into account. Adding an elliptic regularisation, depending on a relaxation parameter $\delta>0$, in the equation for the chemical potential, we prove the existence of a weak solution to an initial and boundary value problem for the relaxed system. Then, we let $\delta$ go to zero, and we recover the existence of a weak solution to the original system.

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Cecilia Cavaterra, Matteo Fornoni, Maurizio Grasselli, Benoît Perthame. 2025-12-17. On a relaxed Cahn-Hilliard tumour growth model with single-well potential and degenerate mobility. https://arxiv.org/abs/2512.15426

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