| Project/Area Number |
23740131
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
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| Research Collaborator |
ADACHI Shinji 静岡大学, 工学部, 准教授 (40339685)
SHIBATA Masataka 東京工業大学, 理工学研究科, 助教 (90359688)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 大域解析学 / 関数方程式論 / 変分法 / 準線形方程式 |
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| Outline of Final Research Achievements |
In this research, we 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 when the parameter is sufficiently large or sufficiently small, we were able to solve the uniqueness problem, which was left open up to now. As to the asymptotic behavior, we proved that it changes drastically depending on the exponent of the nonlinear term. A feature of this research was to focus on a “dual variational” structure of the equation and to clarify its correspondence.
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