| Abstract: |
| We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn--Hilliard type equation that describes the phase separation process between healthy and tumour tissue. This equation is coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of forces, including inertial and viscous effects. The main novelty is the introduction of tissue damage, whose evolution is ruled by a parabolic differential inclusion. We prove a global-in-time existence result for weak solutions by passing to the limit in a time-discretized and regularized version of the system. |
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