Interfaces and Free Boundaries


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Volume 7, Issue 2, 2005, pp. 147–159
DOI: 10.4171/IFB/118

Published online: 2005-06-30

Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors

Shangbin Cui[1]

(1) Zhongshan University, Guangzhou, Guangdong, China

In this paper we study a free boundary problem of a reaction diffusion equation modeling the growth of necrotic tumors. We first reduce this problem into an equivalent initial boundary value problem for a nonlinear parabolic equation on a fixed domain. This parabolic equation is strongly singular in the sense that not only it contains a discontinuous nonlinear function of the unknown function, but also all its coefficients are discontinuous nonlinear functionals of the unknown function. We use approximation method and the Schauder fixed point theorem combined with $L^p$ estimates to prove the existence of a global solution.

Keywords: Free boundary problem, tumor growth, global solution, existence

Cui Shangbin: Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors. Interfaces Free Bound. 7 (2005), 147-159. doi: 10.4171/IFB/118