IJPAM: Volume 28, No. 3 (2006)

GLOBAL EXISTENCE FOR A FREE BOUNDARY PROBLEM
MODELLING THE GROWTH OF NECROTIC TUMORS IN
THE PRESENCE OF INHIBITORS

Xuemei WeiDepartment of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong, 510090, P.R. CHINA
Department of Applied Mathematics
Guangdong University of Technology
Guangzhou, Guangdong, 510090, P.R. CHINA
and
Department of Mathematics
Sun Yat-Sen University
Guangzhou, Guangdong, 510275, P.R. CHINA
e-mail: wxm_gdut@163.com


Abstract.In this paper we study a free boundary problem modelling the growth of necrotic tumors in the presence of inhibitors. By transforming this free boundary problem into an initial-boundary value problem in a fixed domain of a coupled system of two parabolic equations and one integro-differential equation, in which all equations involve discontinuous terms, and using the approximation method combined with the Schauder Fixed Point Theorem and the $L^p$-theory for parabolic equations, we prove that this problem has a global solution in any given time interval $[0,T]$.

Received: March 31, 2006

AMS Subject Classification: 35K35, 35Q80, 35R05

Key Words and Phrases: free boundary problem, tumor growth, global solution, existence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 3