2009 Fiscal Year Final Research Report
Study on collision phenomena of blow-up points appear in Liouville systems and those of vortices
| Project/Area Number |
19540222
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | University of Miyazaki |
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Principal Investigator |
OHTSUKA Hiroshi University of Miyazaki, 工学部, 准教授 (20342470)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJIKAWA Tohru 宮崎大学, 工学部, 教授 (10258288)
SEKIGUCHI Masayoshi 木更津工業高等専門学校, 基礎学系, 教授 (30236088)
SENBA Takashi 九州工業大学, 工学研究院, 教授 (30196985)
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| Research Collaborator |
SUZUKI Takashi 大阪大学, 大学院・基礎工学研究科, 教授
TONIA Ricciardi ナポリ大学, 数学科, 准教授
MASSIMO Grossi ローマ大学, 数学科, 准教授
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| Project Period (FY) |
2007 – 2009
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| Keywords | 関数方程式論 / 関数解析学 / 応用数学 / 数理物理 / Liouville system / 変分法 / 渦点 / 点渦 |
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| Research Abstract |
I studied the mean field equation of vortices with mixed intensities, which is one important example of Liouville systems and got "a mass identity" as a basic fact to classify the collisions of the blow-up points. In addition, I established technique to estimate the Morse index of the critical point about the certain functional that could not assume the Palais-Smale condition including the functionals that lead Liouville systems. Furthermore, I showed a property about the structure around the critical point called "the asymptotic non-degeneracy" about the functionals relating to the scalar Liouville systems (i.e., the Liouville type equations).
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