Cahn-Hilliard-Brinkman model for tumor growth with possibly singular potentials

Abstract

We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The main novelty of the paper concerns the discussion of the existence of weak solutions to the system covering all the meaningful cases for the nonlinear potentials; in particular,the typical choices given by the regular, the logarithmic, and the double obstacle potentials are admitted in our treatise. Compared to previous results related to similar models, we suggest, instead of the classical no-flux condition, a Dirichlet boundary condition for the chemical potential appearing in the Cahn-Hilliard-type equation. Besides, abstract growth conditions for the source terms that may depend on the solution variables are postulated.

References in corpus (4)

• A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
• On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
• On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
• On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

Cited by in corpus (1)

• Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions