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Mathematical Problems in Engineering
Volume 2014, Article ID 480147, 9 pages
Research Article

Global Existence and Uniqueness of Solutions for a Free Boundary Problem Modeling the Growth of Tumors with a Necrotic Core and a Time Delay in Process of Proliferation

School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, China

Received 7 March 2014; Revised 29 April 2014; Accepted 11 May 2014; Published 29 May 2014

Academic Editor: Hak-Keung Lam

Copyright © 2014 Shihe Xu and Minhai Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a mathematical model for the growth of necrotic tumors with time delays in proliferation. By transforming this problem into an initial-boundary value problem in fixed domain of a coupled system of a parabolic equation and one integrodifferential equation with time delays, in which all equations involve discontinuous terms, and using the approximation method combined with Schauder fixed point theorem, we prove that this problem has a unique global solution in any time interval .