Analysis of a solid avascular tumor growth model with time delays in proliferation process

摘要

In this paper we study a free boundary problem modeling solid avascular tumor growth. The model is based on the reaction-diffusion dynamics and mass conservation law. The model is considered with time delays in proliferation process. The quasi-steady-state (i.e., d=0) is studied by Fory? and Bodnar [see U. Fory?, M. Bodnar, Time delays in proliferation process for solid avascular tumour, Math. Comput. Modelling 37 (2003) 1201-1209]. In this paper we mainly consider the case d>0. In the case considered by Fory? and Bodnar, the model is reduced to an ordinary differential equation with time delay, but in the case d>0 the model cannot be reduced to an ordinary differential equation with time delay. By L ~p theory of parabolic equations and the Banach fixed point theorem, we prove the existence and uniqueness of a local solutions and apply the continuation method to get the existence and uniqueness of a global solution. We also study the long time asymptotic behavior of the solutions under some conditions.