A free boundary problem for an elliptic-parabolic system: Application to a model of tumor growth

被引：55

作者：

Bazaliy, BV

Friedman, A

机构：

[1] Univ Minnesota, Dept Math, Minneapolis, MN 55455 USA

[2] Natl Acad Sci, Inst Appl Math & Mech, Donetsk, Ukraine

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2003年 / 28卷 / 3-4期

关键词：

elliptic-parabolic system; elliptic variational inequality; free boundary problem; tumor growth;

D O I：

10.1081/PDE-120020486

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study a free boundary problem for a system of two partial differential equations, one parabolic and other elliptic. The system models the growth of a tumor with arbitrary initial shape. We establish the existence and uniqueness of a solution for some time interval. In the special case where we only have the elliptic equation, the problem coincides with the Hele-Shaw problem.

引用

页码：517 / 560

页数：44

共 15 条

[1]

Adams A, 2003, SOBOLEV SPACES

[2]

[Anonymous], ANN SCUOLA NORM SUP

[3]

Bazaliy B. V., 1997, UKR MATH J, V40, P1465

[4] Growth of necrotic tumors in the presence and absence of inhibitors [J].