Geodesic
A Hyperbolic Free Boundary Problem Modeling Tumor Growth
Shangbin Cui1 ; Avner Friedman2
1Zhongshan University, Guangzhou, Guangdong, China
2Ohio State University, Columbus, USA
Interfaces and free boundaries, Tome 5 (2003) no. 2, pp. 159-182

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DOI

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<KR​<∞, KR​=0 and KR​=∞, where KR​ is the removal rate of dead cells. We also prove that in the cases 0<KR​<∞ and KR​=∞ there exist positive numbers δ0​ and M such that δ0​≤R(t)≤M for all t≥0, while limt→∞​R(t)=∞ in the case KR​=0.
DOI : 10.4171/ifb/76
Classification : 46-XX, 60-XX
Mots-clés : Tumor growth; proliferating cells; quiescent cells; dead cells; free boundary problem; global solution

Shangbin Cui  1   ; Avner Friedman  2

1 Zhongshan University, Guangzhou, Guangdong, China
2 Ohio State University, Columbus, USA 
Shangbin Cui; Avner Friedman. A Hyperbolic Free Boundary Problem Modeling Tumor Growth. Interfaces and free boundaries, Tome 5 (2003) no. 2, pp. 159-182. doi: 10.4171/ifb/76
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     title = {A {Hyperbolic} {Free} {Boundary} {Problem} {Modeling} {Tumor} {Growth}},
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     year = {2003},
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