| Project/Area Number |
15K04996
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
矢崎 成俊 明治大学, 理工学部, 専任教授 (00323874)
中村 俊子 (荻原俊子) 城西大学, 理学部, 教授 (70316678)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 界面ダイナミクス / 進行波 / 移動境界問題 / 順序保存力学系 / 無条件安定性 |
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| Outline of Final Research Achievements |
In order to understand step dynamics on crystal surfaces, from the viewpoint of mathematical and numerical analysis, we investigated front interaction arising in reaction-diffusion equations with multistable nonlinear terms. We also studied the relationship between the monotonicity of the profile of traveling fronts and their stability for related spatially discrete models in the framework of order-preserving dynamical systems. Furthermore, we developed several numerical computation schemes to track the time evolution of interfaces and free boundaries efficiently and accurately.
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| Academic Significance and Societal Importance of the Research Achievements |
観測技術の進歩により詳細に調べられるようになった結晶表面のステップと呼ばれるわずか1原子層の高さしかない段差の時間変化について，多重安定型非線形項を持つ反応拡散方程式による定性的モデルの数学解析・数値解析を行い，微斜面に並ぶステップの空間パターンの形成メカニズムに関する新たな知見を得ることができた．また，本研究で開発した界面現象や自由境界を効率的に精度よく追跡する数値スキームは，今後の他の問題への適用が期待できる汎用的な手法であり，学術的意義のあるものである．
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