| Project/Area Number |
15K04970
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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 |
Mathematical analysis
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
足達 慎二 静岡大学, 工学部, 教授 (40339685)
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| Research Collaborator |
SHIBATA Masataka 東京工業大学, 理工学研究科, 助教 (90359688)
YAGISHITA Hiroki 京都産業大学, 理学部, 教授 (80349828)
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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 |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
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| Keywords | 非線形解析 / 変分問題 / 楕円型偏微分方程式 / 安定性解析 / 準線形方程式 |
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| Outline of Final Research Achievements |
In this research, I have studied a quasilinear Schrodinger equation arising in plasma physics. This equation describes behavior of wave functions spreading through “superfluid films”, which are applied to polymer film coatings. The main results of this research were to analyze the uniqueness and the asymptotic behavior with respect to a physical parameter of ground states for an elliptic partial differential equation which appears as a stationary problem. Especially we were able to obtain the uniqueness without any restriction on the parameter, and performed a complete classification of asymptotic behavior depending on the size of an exponent of the nonlinear term.
I have also performed the stability analysis of standing waves for the Schrodinger-Maxwell system which appears in the Gauge theory, and investigated several other physical models.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の問題意識は物理学者による考察を数学的に厳密化することであり、応用面でも大きな意義があると考えている。定在波解は様々な数理モデルにおいて現れ、その安定性解析は重要な研究課題の一つであるが、厳密な解析が行われていない数理モデルは数多く残されている。本研究が目的とするラグランジュ乗数のパラメータ依存性問題に対する解析手法の確立は、定在波解の安定性解析の研究において新たな試みであり、理論面からも応用面からも重要であると考えている。
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