Abstract
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumor cells coupled to a reaction-diffusion-type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip the system with a Neumann boundary condition for the tumor cell variable and the chemical potential, a Robin-type boundary condition for the nutrient, and a ...
Abstract
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumor cells coupled to a reaction-diffusion-type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip the system with a Neumann boundary condition for the tumor cell variable and the chemical potential, a Robin-type boundary condition for the nutrient, and a "no-friction" boundary condition for the velocity, which allows us to consider solution-dependent source terms. Well-posedness of the model as well as existence of strong solutions will be established for a broad class of potentials. We will show that in the singular limit of vanishing viscosities we recover a Darcy-type system related to Cahn-Hilliard-Darcy-type models for tumor growth which have been studied earlier. An asymptotic limit will show that the results are also valid in the case of Dirichlet boundary conditions for the nutrient.
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