A rigorous sharp interface limit of a diffuse interface model related to tumor growth
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 , 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 [A. Hawkins-Daruud, K. G. van der Zee, J. T. Oden, Numerical simulation of a thermodynamically consistent four-species tumor growth model, Int. J. Numer. Math. Biomed. Engng. 28 (2011), 3--24.] (cf. also [D. Hilhorst, J. Kampmann, T. N. Nguyen, K. G. van der Zee, Formal asymptotic limit of a diffuse-interface tumor-growth model, Math. Models Methods Appl. Sci. 25 (2015), 1011--1043.]). Exploiting the techniques related to both gradient-flows and gamma convergence, we recover a condition on the interface relating the chemical and double-well potentials, the mean curvature, and the normal velocity.
Cite
@article{arxiv.1606.04663,
title = {A rigorous sharp interface limit of a diffuse interface model related to tumor growth},
author = {E. Rocca and R. Scala},
journal= {arXiv preprint arXiv:1606.04663},
year = {2016}
}