| Project/Area Number |
25400134
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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 |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
TANAKA Naoki 静岡大学, 理学部, 教授 (00207119)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMIZU Senjo 京都大学, 人間・環境学研究科, 教授 (50273165)
ISHII Katsuyuki 神戸大学, 海事科学研究科, 教授 (40232227)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Toshitaka 静岡大学, 理学部, 教授 (20229561)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | evolution operator / metric-like functional / connectedness condition / subtangential condition / dissipativity condition / monotone operator / Lipschitz semigroup / comparison function / dissipativity / connected condition / weak continuity / revel set / quasilinear equation / Favard class / semigroup of operators / delay equation / 退化準線形発展方程式 / リプシッツ発展作用素 / 非自励な方程式系 |
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| Outline of Final Research Achievements |
We characterize the well-posedness for nonautonomous differential equations governed by continuous operators, using dissipativity conditions with respect to metric-like functionals, subtangential conditions and connectedness conditions. Toward to the non-continuous case, we generalize the cerebrated well-posedness result on autonomous differential equations governed by maximal monotone operators due to Komura and Brezis. Moreover, we discuss the well-posedness for functional differential equations and the solvability of abstract Cauchy problems for weakly continuous operators.
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