A RIGOROUS APPROACH TO THE SHARP INTERFACE LIMIT FOR PHASE-FIELD MODELS OF TUMOR GROWTH\ast

被引：0

作者：

Riva, Filippo ^{[1
]}

Rocca, Elisabetta ^{[2
]}

机构：

[1] Univ Pavia, Dipartimento Matemat Felice Casorati, I-27100 Pavia, Italy

[2] Univ Pavia, IMATI CNR, Dipartimento Matemat Felice Casorati, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2025年 / 57卷 / 01期

关键词：

Cahn--Hilliard equation; reaction-diffusion equation; sharp interface; diffuse interface; asymptotics; tumor growth; varifolds; CAHN-HILLIARD EQUATION; MEAN-CURVATURE FLOW; LONG-TIME BEHAVIOR; GAMMA-CONVERGENCE; WELL-POSEDNESS; DARCY SYSTEM; CHEMOTAXIS;

D O I：

10.1137/24M1644523

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider two diffuse interface models for tumor growth coupling a 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 Appl. Sci., 26 (2016), pp. 1095--1148]. 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.

引用

页码：65 / 94

页数：30

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