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

作者：Garcke, Harald^*; Lam, Kei Fong

来源：European Journal of Applied Mathematics, 2017, 28(2): 284-316.

DOI：10.1017/S0956792516000292

• Tumour growth
• phase field model
• Cahn-Hilliard equation
• reaction-diffusion equations
• chemotaxis
• weak solutions
• well-posedness

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.

• 出版日期2017-4