A Rigorous Sharp Interface Limit of a Diffuse Interface Model Related to Tumor Growth

In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter ε, representing the interface thickness between the tumorous and non tumorous cells, tends to zero. More in particular, we analyze here a gradient-flow type model arising from a modification of the recently introduced model for tumor growth dynamics in [21] (cf. also [22]). Exploiting the techniques related to both gradient-flows and gamma convergence, we recover a condition on the interface Γ relating the chemical and double-well potentials, the mean curvature, and the normal velocity.