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Existence and uniqueness of global solutions of a free boundary problem modeling tumor growth. (Chinese. English summary) Zbl 1220.35198

The authors study the general nonnecrotic tumor growth model proposed by H. M. Byrne and M. A. J. Chaplain [Math. Biosci. 130, 151–181 (1995; Zbl 0836.92011)] 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.

MSC:

35R35 Free boundary problems for PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C50 Medical applications (general)

Citations:

Zbl 0836.92011
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