关于肿瘤细胞破坏并入侵正常组织或细胞质基质的数学模型的分析  

Analysis of a Mathematical Modeling of Cancer Cell Breakout and Invasion of Normal Tissue or Extracellular Matrix

作　　者：张久远[1] 冯兆永[2] 刘成霞[3] 卫雪梅[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510006 [2]中山大学数学与计算科学学院,广东广州510275 [3]广东省口腔医院,广东广州510280

出　　处：《中山大学学报（自然科学版）》2013年第3期48-54,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(11101095)

摘　　要：固体肿瘤的生长分为两个阶段:未血管化阶段和血管化阶段。未血管化阶段的肿瘤处于扩散受到限制的休眠期,直径只有几毫米,而在血管化阶段肿瘤发生浸润和转移。主要研究了织肿瘤细胞破坏并入侵正常组织或细胞质基质的数学模型。这个模型包含了四个含有交叉扩散的抛物方程和一个退化的抛物方程。通过应用抛物型方程的Lp理论、Schauder估计、比较原理和Banach不动点定理,证明了这个模型整体解的存在唯一性。The growth and development of solid tumors occurs in two distinct phases： the avascular and the vascular phase. During the former growth phase the tumor remains in a diffusion-limited dormant state of a few millimeters in diameter, while during the later phase, invasion and metastasis do take place. A mathematical model of cancer cell breakout and invasion of normal tissue or extracellular matrix is stud- ied. The model consists of a system of four Reaction-diffusion-taxis partial differential equations and a de- generate parabolic partial differential equations. By using the parabolic Lp -theory, the parabolic Schauder estimates, principle of comparison and the Banach fixed point theorem, it is proved that this system has a unique global solution.

关 键 词：肿瘤生长 局部解 整体解 

分 类 号：O175.2[理学—数学]