2016 Fiscal Year Final Research Report
Studies of the interface motion and the signal propagation mechanism in the bidomain model
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 |
Research Field |
Mathematical analysis
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Research Institution | The University of Tokyo |
Principal Investigator |
Matano Hiroshi 東京大学, 大学院数理科学研究科, 教授 (40126165)
|
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
|
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 |
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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Free Research Field |
非線形解析学
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