A Hyperbolic Free Boundary Problem Modeling Tumor Growth
Shangbin Cui
Zhongshan University, Guangzhou, Guangdong, ChinaAvner Friedman
Ohio State University, Columbus, USA
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Abstract
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 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 , and , where is the removal rate of dead cells. We also prove that in the cases and there exist positive numbers and such that for all , while in the case .
Cite this article
Shangbin Cui, Avner Friedman, A Hyperbolic Free Boundary Problem Modeling Tumor Growth. Interfaces Free Bound. 5 (2003), no. 2, pp. 159–182
DOI 10.4171/IFB/76