Analysis of a solid avascular tumor growth model with time delays in proliferation process
作者： Shihe Xu , Meng Bai , Xiangqing Zhao
DOI: 10.1016/J.JMAA.2012.02.034
关键词: Calculus 、 Process (computing) 、 Applied mathematics 、 Uniqueness 、 Banach fixed-point theorem 、 Free boundary problem 、 Stability (probability) 、 Ordinary differential equation 、 Conservation of mass 、 Mathematics 、 Parabolic partial differential equation
摘要: Abstract 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. considered with time delays in proliferation process. quasi-steady-state (i.e., d = 0 ) studied by Foryś Bodnar [see U. Foryś, M. Bodnar, Time process for tumour, Math. Comput. Modelling 37 (2003) 1201–1209]. mainly consider case > . reduced to an ordinary differential equation delay, but cannot be delay. By L p theory of parabolic equations Banach fixed point theorem, prove existence uniqueness local solutions apply continuation method get global solution. We also long asymptotic behavior under some conditions.
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