论文标题
癌症入侵模型的经典解决方案的全球存在和数值模拟
Global existence of classical solutions and numerical simulations of a cancer invasion model
论文作者
论文摘要
在本文中，我们从理论和数字上研究了癌症入侵模型。该模型是一个非平稳的非线性系统，该系统由三个耦合的部分微分方程，对癌细胞的运动，细胞外基质的降解和某些酶进行降解。尽管缺乏基质降解酶的扩散以及在分析处理中的相应正则效应，但我们首先在二维和三维有界结构域中建立了全球经典溶液的存在。接下来，我们给出一个弱的公式，并应用有限的时间差异和galerkin有限元方案进行空间离散化。总体算法基于定点迭代方案。为了证实我们的理论和数值框架，在两个和三个空间维度中进行了几个数值模拟。
In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. We first establish existence of global classical solutions in both two- and three-dimensional bounded domains, despite the lack of diffusion of the matrix-degrading enzymes and corresponding regularizing effects in the analytical treatment. Next, we give a weak formulation and apply finite differences in time and a Galerkin finite element scheme for spatial discretization. The overall algorithm is based on a fixed-point iteration scheme. In order to substantiate our theory and numerical framework, several numerical simulations are carried out in two and three spatial dimensions.
