2011 Fiscal Year Final Research Report
Functional analytic research of hyperbolic equations with memory
| Project/Area Number |
20540154
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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 |
Basic analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
OKA Hirokazu 茨城大学, 工学部, 教授 (90257254)
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| Co-Investigator(Kenkyū-buntansha) |
HIRASAWA Go 茨城大学, 工学部, 教授 (10434002)
UEKI Seiichirou 茨城大学, 工学部, 准教授 (70512408)
HOSOKAWA Takuya 茨城大学, 工学部, 准教授 (90553579)
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| Co-Investigator(Renkei-kenkyūsha) |
TANAKA Naoki 静岡大学, 理学部, 教授 (00207119)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 準線形双曲型方程式 / リプシッツ作用素半群 / 半線形発展方程式 / q-変形正規作用素 / 解析関数空間 / 荷重合成作用素 / Bloch空間 |
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| Research Abstract |
A hyperbolic equation with memory and its related field are studied from the viewpoint of both sides of theory consideration to deal with the equation generally and systematically and the functional space in which the equation works place. As a result, abstract theories are developed to get global classical solutions for qualinear/semilinear evolution equations, and the characterizations are obtained of weighted composition operators on analytic function spaces and on the Bloch space. We also provided with the characterization of the contraction which corresponds injectively to the q-deformed normal operator.
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