Research on the Solution of Cell Invasion Model with Free Boundary

• 作者: Ahmadjan Muhammadhaji Rouzimaimaiti Mahemuti Takashi Suzuki
• 来源期刊: 应用科学(英文)
• 学科: 数学
• 关键词: INVADOPODIA CANCER Stefan PROBLEM Free BOUNDARY
• 年，卷（期）: 2017,（6）
• 页码范围: 242-261
• 页数: 20页
• 分类号: O1

摘要

There are many works (i.e. [1]) aiming to find out numerically how positive feedback affects the formation of invadopodia and invasion of cancer cells;however, studies on the cancer cell invasion model with free boundary are fairly rare. In this paper, we study modified cancer cell invasion model with free boundary, where, free boundary stands for cancer cell membrane, so that we can more precisely describe the positive feedback affects. Firstly, we simplized the model by means of characteristic curve and semi-groups’ property, and obtained the Stefan-like problem by introducing Gaussian Kernel and Green function. Secondly, based on the classical Stefan problem, we derived the integral solution of simplified model, which could lead us a further step to find the solution of modified cancer cell invasion model.