Calculus of Variations and Geometric Measure Theory

F. Riva - E. Rocca

A rigorous approach to the sharp interface limit for phase-field models of tumor growth

created by riva on 01 Mar 2024



Inserted: 1 mar 2024
Last Updated: 1 mar 2024

Year: 2024

ArXiv: 2402.19156 PDF


In this paper we consider two diffuse interface models for tumor growth coupling a Cahn-Hilliard type equation for the tumor phase parameter to a reaction-diffusion type equation for the nutrient. The models are distinguished by the presence of two different coupling source terms. For such problems, we address the question of the limit, as the diffuse interface parameter tends to zero, from diffuse interface models to sharp interface ones, justifying rigorously what was deduced via formal asymptotics in 18. The resulting evolutions turn out to be varifold solutions to Mullins-Sekerka type flows for the tumor region suitably coupled with the equation for the nutrient.

Keywords: varifolds, Cahn-Hilliard equation, sharp interface, diffuse interface, Reaction-diffusion equation, Asymptotics, Tumor growth