一个肿瘤化疗数学模型的分析

这里考虑一个刻画血管化肿瘤的化学治疗的数学模型.该模型是一个偏微分方程系统的自由边界问题.系统的未知变量有：肿瘤细胞内部的药物浓度;对药物敏感的和具有耐药性的肿瘤细胞密度;肿瘤细胞运动的速度场;自由边界（即肿瘤边界）.本文对该模型进行严格的数学分析,从理论上探索对肿瘤成功治疗时药物浓度所满足的条件.

Mathematical Analysis of a Model of a Vascular Tumor with Chemotherapy

In this paper we consider a mathematical model that describes the evolution of a vascular tumor in response to chemotherapeutic treatment. The model is a free boundary problem for a system of partial differential equations. The unknown variables of the system are : the densities of the cells that are highly susceptible to the drug, the cells that have lower drug susceptibility, and the intratumoral drug concentration, and the volocity of cells within the tumor as well as free boundary. The purpose of this paper is to establish a rigorous mathematical analysis of the model, and to explore the explicit condition of the prescribed drug concentration in the tumor vasculature for successful treatment of a tumor.