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arXiv · 1511.06143

Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport

Harald Garcke·Kei Fong Lam
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Abstract

We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the presence of a nutrient species and surrounded by healthy tissue. The model also takes into account transport mechanisms such as chemotaxis and active transport. We establish well-posedness results for the tumour model and a variant with a quasi-static nutrient. It will turn out that the presence of the source terms in the Cahn--Hilliard equation leads to new difficulties when one aims to derive a priori estimates. However, we are able to prove continuous dependence on initial and boundary data for the chemical potential and for the order parameter in strong norms.

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Harald Garcke, Kei Fong Lam. 2016-05-25. Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport. https://arxiv.org/abs/1511.06143

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