中文摘要：

该文研究一个反应扩散方程组的自由边界问题，它来源于描述抑制物作用下无坏死核肿瘤生长的数学模型．作者运用抛物型方程的L^P理论和压缩映照原理，证明了这个问题局部解的存在唯一性，然后用延拓方法得到了整体解的存在唯一性．

英文摘要：

In this paper the authors study the general nonnecrotic tumor growth model proposed by Byrne and Chaplain in 1995. 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.