Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 03, pp. 118.
A parabolichyperbolic free boundary problem modeling
tumor growth with drug application
JiHong Zhao
Abstract:
In this article, we study a free boundary problem modeling the
growth of tumors with drug application. The model consists
of two nonlinear secondorder parabolic equations describing
the diffusion of nutrient and drug concentration,
and three nonlinear firstorder hyperbolic equations describing
the evolution of proliferative cells, quiescent cells and
dead cells. We deal with the radially symmetric case of this free
boundary problem, and prove that it has a unique global solution.
The proof is based on the L^p theory of parabolic equations,
the characteristic theory of hyperbolic equations and the Banach
fixed point theorem.
Submitted August 10, 2009. Published January 6, 2010.
Math Subject Classifications: 35Q80, 35L45, 35R05.
Key Words: Parabolichyperbolic equations;
free boundary problem; tumor growth; global solution.
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JiHong Zhao
School of Mathematics and Computional Science
Sun YatSen University, Guangzhou, Guangdong, 510275, China
email: zhaojihong2007@yahoo.com.cn

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