2018 Fiscal Year Final Research Report
Qualitative study on model equations arising in mathematical biology from a viewpoint of the bifurcation theory
| Project/Area Number |
17KK0086
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| Research Category |
Fund for the Promotion of Joint International Research (Fostering Joint International 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 |
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| Research Collaborator |
Hilhorst Danielle Centre National de la Recherche Scientifique(CNRS)/Université de Paris-Sud, Départment de Mathématiques d'Orsay, Emeritus Directrice de recherche au CNRS
Bataillon Chirstian
Bouguezzi Meriem
Lequien Florence
Rouillard Fabien
Scheid Jean-Francois
Matano Hiroshi
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| Project Period (FY) |
2018
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| Keywords | 楕円型偏微分方程式 / 放物型偏微分方程式 / 分岐理論 / 自由境界問題 / 一層ステファン問題 |
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| Outline of Final Research Achievements |
We propose a mathematical model, which is a system of partial differential equations, in order to clarify the mechanism of corrosion of a material, and study qualitative properties of a solution by numerical simulation. We also study a simplified model mathematically.
Specifically, we construct a full model and do numerical simulations. Since the full model is difficult to analyze mathematically, we start to study a one-dimensional problem of a simplified equation and give a proof of mathematical properties.
The simplified model is equivalent to the classical one-phase Stefan problem, and hence the existence and uniqueness of solution hold. We also study an asymptotic behavior of the solution.
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| Free Research Field |
偏微分方程式
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| Academic Significance and Societal Importance of the Research Achievements |
金属の腐食現象のメカニズムを解明することによって，材料の劣化に対抗し，適切な材料の保護の方法を確立する手助けとなることが期待される．そして，それは使用済みの放射性廃棄物を詰めた容器の腐食の問題などに，応用が可能であると期待される．
また，数学的には，長い研究の歴史がある1層ステファン問題に対して，新しい結果（解の漸近挙動）を数学的に証明したこととなり，解の挙動に関して新たな視点を与えた．
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