Global well-posedness for a drug transport model in tumor multicell spheroids

In this paper we study global existence of solutions of a mathematical model for drug transport in tumor multicell spheroids. The model is a free boundary problem of a system of partial differential equations. It contains one nonlinear first-order equation describing the distribution of live tumor cells, and two nonlinear reaction diffusion equations describing the evolution of nutrient concentration and drug concentration, respectively. By using the method of characteristics for first-order equations, the LpLp-theory for parabolic equations, the Banach fixed point theorem and the extension method, we prove that this problem has a unique global solution.