Traveling waves of a free boundary problem related to amoeba motility

2014 Fiscal Year Final Research Report

• Project/Area Number: 24840039
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Meiji University
• Principal Investigator: MONOBE harunori 明治大学, 公私立大学の部局等, 研究員 (20635809)
• Project Period (FY): 2012-08-31 – 2015-03-31
• Keywords: 自由境界問題 / 進行波解 / 細胞運動

Outline of Final Research Achievements

In this study, I analyzed a free boundary problem related to cell motility and showed that there exists at least two traveling wave solutions for the problem, where traveling wave solution means that the solution moves to a direction with a constant speed and shape. This result implies that a cell moves to a direction with a constant shape and speed. This motion is observed in keratocyte. I also showed that there exist just two stationary solutions which are radially symmetric. This means that a shape of cell is approaches a disk-shaped domain as time passes. To describe the behavior of solutions to the free boundary problem by computer, I tried to approximate the free boundary problem with the help of reaction-diffusion system. However it was difficult. Thus, I attempted to extend theory of fast reaction limit and obtained some results related to fast reaction limit.

Free Research Field

自由境界問題