Variational approach to collision, detachment and adhesion

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340024
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kanazawa University
• Principal Investigator: OMATA Seiro 金沢大学, 数物科学系, 教授 (20214223)
• Co-Investigator(Kenkyū-buntansha): 長山 雅晴 北海道大学, 電子科学研究所, 教授 (20314289)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 偏微分方程式 / 変分問題 / 数値解析 / 双曲型自由境界問題

Outline of Final Research Achievements

We have studied the motion of elastic body, fluid and their interaction. We used energy formula and variational method for solving these problems. The main target was hyperbolic free boundary problems which can be treated the motion of bubble even with junctions.Our method is based on the discrete Morse flow, which is defined by "time difference space differential" type functionals. We have constructed approximate solutions for hyperbolic free boundary problems and in easy cases we could show the existence of the solution.
The other feature of this problem is that we can add global constraints such as volume preserving constraint.We also developed numerical algorithm based on this idea.

Free Research Field

偏微分方程式論