Wei, Xuemei; Cui, Shangbin Existence and uniqueness of global solutions of a free boundary problem modeling tumor growth. (Chinese. English summary) Zbl 1220.35198 Acta Math. Sci., Ser. A, Chin. Ed. 26, No. 1, 1-8 (2006). 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. Reviewer: K. Mathiak (Braunschweig) Cited in 12 Documents MSC: 35R35 Free boundary problems for PDEs 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92C50 Medical applications (general) Keywords:nonnecrotic tumor growth model; reaction-diffusion equations; existence; uniqueness; local solution; global solution Citations:Zbl 0836.92011 PDFBibTeX XMLCite \textit{X. Wei} and \textit{S. Cui}, Acta Math. Sci., Ser. A, Chin. Ed. 26, No. 1, 1--8 (2006; Zbl 1220.35198)