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Interfaces and Free Boundaries

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Volume 5, Issue 2, 2003, pp. 159–182
DOI: 10.4171/IFB/76

Published online: 2003-06-30

A Hyperbolic Free Boundary Problem Modeling Tumor Growth

Shangbin Cui[1] and Avner Friedman[2]

(1) Zhongshan University, Guangzhou, Guangdong, China
(2) Ohio State University, Columbus, USA

In this paper we study a free boundary problem modeling the growth of tumors with three cell populations: proliferating cells, quiescent cells and dead cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, with tumor surface as a free boundary. The nutrient concentration satisfies a diffusion equation, and the free boundary $r=R(t)$ satisfies an integro-differential equation. We consider the radially symmetric case of this free boundary problem, and prove that it has a unique global solution for all the three cases $0

Keywords: Tumor growth; proliferating cells; quiescent cells; dead cells; free boundary problem; global solution

Cui Shangbin, Friedman Avner: A Hyperbolic Free Boundary Problem Modeling Tumor Growth. Interfaces Free Bound. 5 (2003), 159-182. doi: 10.4171/IFB/76