Speaker
Description
A diffuse interface model for tumour growth in the presence of a nutrient is introduced, incorporating mechanical effects and reversible tissue damage. The highly nonlinear PDE system consists of a Cahn–Hilliard equation governing the phase separation between healthy and tumour cells, coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of linear momentum, accounting for inertial and viscous effects. The main novelty is the presence of tissue damage, whose evolution is governed by a parabolic differential inclusion. A global-in-time existence result for weak solutions is established via a time-discretization and regularization argument. Finally, the obstructions to uniqueness are discussed.