Singular limit of the porous medium equation with a drift

被引：16

作者：

Kim, Inwon ^{[1
]}

Pozar, Norbert ^{[2
]}

Woodhouse, Brent ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Kanazawa Univ, Fac Math & Phys, Inst Sci & Engn, Kanazawa, Ishikawa 9201192, Japan

来源：

ADVANCES IN MATHEMATICS | 2019年 / 349卷

基金：

日本学术振兴会;

关键词：

Porous medium equation; Hele-Shaw problem; Singular limit; Viscosity solutions; Tumor growth; HELE-SHAW PROBLEM; VISCOSITY SOLUTIONS; DIFFUSION; REGULARITY; UNIQUENESS; EXISTENCE; EVOLUTION; DYNAMICS; FLOWS; MODEL;

D O I：

10.1016/j.aim.2019.04.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in time. In the limit a Hele-Shaw-type free boundary problem emerges, which describes the evolution of the congested zone where density equals one. We discuss pointwise convergence of the densities as well as the BV regularity of the limiting free boundary. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：682 / 732

页数：51

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