Analysis of a free boundary problem modeling tumor growth (Q2581242)

We study a free boundary problem arising from the modelling 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 integro-differential 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 \(t\to\infty\).