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

2024/02/29 by Filippo Riva, Riva, Filippo, Elisabetta Rocca +1 · 2 citations
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2402.19156

openalex publication_date 2024/02/29 · openalex created_date 2024/08/03 · openalex updated_date 2026/07/28

Abstract

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 [20]. 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.

Cited by

• Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
• Phase-Field Modeling of Border Cell Cluster Migration in Drosophila

Related

• Sharp interface limit of a diffuse interface model for tumor-growth
• Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth
• Analysis of a diffuse interface model of multispecies tumor growth
• On a diffuse interface model of tumor growth
• On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport