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

Abstract

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 [0,T]. © 2014 Shihe Xu and Minhai Huang.