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https://doi.org/10.1201/9780203494899.ch10

has been cited by the following article:

• TITLE: Research on the Solution of Cell Invasion Model with Free Boundary

  AUTHORS: Rouzimaimaiti Mahemuti, Ahmadjan Muhammadhaji, Takashi Suzuki

  KEYWORDS: Invadopodia, Cancer, Stefan Problem, Free Boundary

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.7 No.6, June 19, 2017

  ABSTRACT: 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.