A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior

Authors:
Xinfu Chen, Shangbin Cui and Avner Friedman

Journal:
Trans. Amer. Math. Soc. **357** (2005), 4771-4804

MSC (2000):
Primary 34B15; Secondary 35C10, 35Q80, 92C15

Published electronically:
July 20, 2005

MathSciNet review:
2165387

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study a free boundary problem modeling the growth of radially symmetric tumors with two populations of cells: proliferating cells and quiescent cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, and the tumor's surface is a free boundary . The nutrient concentration satisfies a diffusion equation, and satisfies an integro-differential equation. It is known that this problem has a unique stationary solution with . We prove that (i) if , then , and (ii) the stationary solution is linearly asymptotically stable.

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Additional Information

**Xinfu Chen**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Email:
xinfu@pitt.edu

**Shangbin Cui**

Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou, Guangdong 510275, People’s Republic of China

Email:
mcinst@zsu.edu.cn

**Avner Friedman**

Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210-1174

Email:
afriedman@mbi.osu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-05-03784-0

Keywords:
Tumor growth,
free boundary problem,
stationary solution,
asymptotic behavior

Received by editor(s):
September 24, 2002

Published electronically:
July 20, 2005

Article copyright:
© Copyright 2005
American Mathematical Society