Interfaces and Free Boundaries
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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