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

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