Analysis of a Free Boundary Problem Modeling Tumor Growth

In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions: R = R(t), the radius of the tumor, and u = u(r, t), the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 < r < R(t), t > 0, and the function R satisfies a nonlinear integrodi fferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t . ..