# A rigorous sharp interface limit of a diffuse interface model related to tumor growth

created by scala on 09 Jun 2016
modified on 24 Oct 2016

[BibTeX]

Preprint

Inserted: 9 jun 2016
Last Updated: 24 oct 2016

Year: 2016

Abstract:

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 $\eps$, representing the interface thickness between the tumorous and non tumorous cells, tends to zero. More in particular, we analyse here a gradient-flow type model arising from a modification of the recently introduced model for tumor growth dynamics in \cite{HZO} (cf. also \cite{Hil}). Exploiting the techniques related to both gradient-flows and gamma-convergence, we recover a condition on the interface $\Gamma$ relating the chemical and double-well potentials, the mean curvature, and the normal velocity.