Abstract: In this paper the authors study the general nonnecrotic tumor growth model proposed by Byrne and Chaplain in 1995. This is a free boundary problem for a system of nonlinear reaction diffusion equations. The authors apply the L_p theory of parabolic equations and the Banach fixed point theorem to prove the existence and uniqueness of a local solution, and apply the continuation method to get the existence and uniqueness of a global solution.

Key words: Tumor growth, Free boundary problem, Global solution, Existence, Uniqueness