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Analysis of a solid avascular tumor growth model with time delays in proliferation process. (English) Zbl 1241.35211

Summary: 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. 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.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K57 Reaction-diffusion equations
35R35 Free boundary problems for PDEs
35B40 Asymptotic behavior of solutions to PDEs
92C50 Medical applications (general)
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