Abstract: In this paper the authors study a mathematical model of the effect of inbitors on the growth of nonnecrotic tumors based on the idea of Byrne and Chaplain. This model is a free boundary problem of a system of nonlinear reaction diffusion equations. The authors apply the monotone method in the theory of reaction diffusion equations combined with the iteration technique of free boundary problems to obtain asymptotic behavior of the solution, and prove that under some general assumptions on the nutrient consumption rate function f, the inhibitor consumption rate function g and the tumor cell proliferation rate function S, the global solution of this problem tends to the trivial stationary solution (which corresponds to the vanishing state of the tumor) in certain situations, and converges to a nontrival stationary solution (which corresponds to the dormant state of the tumor) in certain other situations, as the time goes to infinity.

Key words: Tumor growth, Free boundary problem, Asymptotic behavior