Research on the Solution of Cell Invasion Model with Free Boundary  

作　　者：Rouzimaimaiti Mahemuti Ahmadjan Muhammadhaji Takashi Suzuki 

机构地区：[1]College of Mathematics and System Sciences, Xinjiang University, Urumqi, China [2]Graduate School of Engineering Science, Osaka University, Osaka, Japan

出　　处：《Open Journal of Applied Sciences》2017年第6期242-261,共20页应用科学（英文）

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.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.

关 键 词：INVADOPODIA CANCER Stefan PROBLEM Free BOUNDARY 

分 类 号：O1[理学—数学]