JournalsifbVol. 7, No. 2pp. 147–159

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

  • Shangbin Cui

    Zhongshan University, Guangzhou, Guangdong, China
Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors cover
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Abstract

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 LpL^p estimates to prove the existence of a global solution.

Cite this article

Shangbin Cui, Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors. Interfaces Free Bound. 7 (2005), no. 2, pp. 147–159

DOI 10.4171/IFB/118