Electron. J. Diff. Equ., Vol. 2010(2010), No. 03, pp. 1-18.

A parabolic-hyperbolic free boundary problem modeling tumor growth with drug application

Ji-Hong Zhao

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.

Show me the PDF file (310 KB), TEX file, and other files for this article.

Ji-Hong Zhao
School of Mathematics and Computional Science
Sun Yat-Sen University, Guangzhou, Guangdong, 510275, China
email: zhaojihong2007@yahoo.com.cn

Return to the EJDE web page