  In this work, we study a model consisting of a Cahn-Hilliard-type equation
for the concentration of tumour 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 Neumann boundary for the tumour cell
variable and the chemical potential, Robin-type boundary conditions 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 viscosity we
recover a Darcy-type system related to Cahn-Hilliard-Darcy type models for
tumour 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.

Analysis of PDEs