On the modelling and analysis of tumor growth with phase-field equations of Cahn-Hilliard type

In this talk, we present a system of partial differential equations modelling the growth of tumor cells. We consider the effect of phase separation into proliferative, hypoxic and necrotic phases. Further, we model the invasion due to ECM degradation and the influence of chemotaxis and haptotaxis. We establish the existence of weak solutions in appropriate function spaces via the Faedo-Galerkin method and illustrate the effects of the model on the tumor growth through numerical simulations with finite element approximations.