In this article, we study a free boundary problem modeling the growth of tumors with drug application. The model consists of two nonlinear second-order parabolic equations describing the diffusion of nutrient and drug concentration, and three nonlinear first-order 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: Parabolic-hyperbolic equations; free boundary problem; tumor growth; global solution.
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| Ji-Hong Zhao |
School of Mathematics and Computional Science
Sun Yat-Sen University, Guangzhou, Guangdong, 510275, China
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