| Project/Area Number |
26610028
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Matano Hiroshi 東京大学, 大学院数理科学研究科, 教授 (40126165)
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| Co-Investigator(Kenkyū-buntansha) |
奈良 光紀 岩手大学, 理工学部, 准教授 (90512161)
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| Research Collaborator |
MORI Yoichiro ミネソタ大学, 数学科, 准教授
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | バイドメインモデル / 平面波 / 安定性 / フランク図形 / 擬微分方程式 / 定性的理論 / 非線形問題 / 国際研究者交流（米国） / スペクトル解析 |
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| Outline of Final Research Achievements |
In this research project, we made a detailed study of the stability of planar traveling waves of the bidomain Allen-Cahn equation.
First, we analyzed the linear stability of planar traveling waves using the spectral information. We revealed the relation between the stability of the planar wave under long-wavelength perturbations and the concavity-convexity properties of the Frank diagram. We also derived remarkable results on the linear stability under medium-wavelength perturbations. Next we proved that linear stability implies nonlinear stability.
Our work gives the first successful results on the stability analysis of bidomain models.
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