中文摘要：

研究了一个肿瘤化学治疗反应的空间结构的数学模型，这是一个动力系统模型，它是偏微分方程的自由边界问题。假设肿瘤的繁殖和死亡由局部药物浓度决定。在一些条件下，通过运用抛物方程的口理论、压缩映像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。在另外一些条件下，通过运用反应扩散方程的上、下解方法，得到了：当0〈w≤w^＊时，此模型没有稳态解；当w·〈w〈w时，此模型有唯一的稳态解（ws,，Rs）。

英文摘要：

A mathematical model of the response of spatially structured tumors to chemotherapy ： drug ki- netics is studied. The model is a free boundary problem of a partial differential equation. The tumor is as- sumed to comprise a single cell population which reproduces and dies at a rate dependent on the localdrug concentration. By using the method of the Lp -theory for parabolic equations, the Banach fixed point theorem and the extensions method under some general conditions, it is proved that this problem has a u- nique global solution. And then, by applying upper and lower solution method in the theory of reaction diffusion equations under some other general conditions to obtain the stationary solution. It is proved that if 0 〈 ws w ＊ , there is no stationary solution; If w^＊ 〈 w 〈 @ , there is a unique stationary solution （ws（r） ,Rs） （Rs 〉 0）