Interfaces and Free Boundaries
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Published online: 2005-06-30
Global existence of solutions for a free boundary problem modeling the growth of necrotic tumorsShangbin Cui (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