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

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。

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

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 studied. The model consists of a system of four Reaction diffusion taxis partial differential equations and a degenerate parabolic partial differential equations. By using the parabolic Lp 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.