On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

Abstract

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.

28 pages

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• Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
• On a nonlocal Cahn-Hilliard equation with a reaction term
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Cited by in corpus (4)

• Cahn-Hilliard-Brinkman systems for tumour growth
• Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
• Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions
• Cahn-Hilliard-Brinkman model for tumor growth with possibly singular potentials