Semigroup-theoretic study of identification problem in evolution equations
| Project/Area Number |
25400182
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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 | Tokyo University of Science |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
Yokota Tomomi 東京理科大学, 理学部第一部, 准教授 (60349826)
Yoshii Kentarou 東京理科大学, 理学部第一部, 助教 (00632449)
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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 |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 発展方程式 / 同定問題 / 作用素半群理論 / 角型極大増大作用素 / 双対性写像 / フレシェ微分 / 陰関数定理 / 連鎖律 / 係数同定問題 / 縮小半群 / 極大角型増大作用素 / Frechet 微分 / 一様凸Banach空間 / 角型増大作用素 / 解析的半群 / 拡散係数 / 逆問題 / 国際研究者交流(イタリア) / 無限次元陰関数定理 / 熱方程式の解の存在 / 荷重ルベーグ空間 / シュレーディンガー型作用素 / 極大増大性 |
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| Outline of Final Research Achievements |
We are concerned with linear evolution equations of parabolic type (d/dt)u(t)+νAu(t) = 0 (0<t<T), where A-ω (ω>0) is an m-sectorial operator in a Banach space X and the coefficient ν＞０ is a parameter. The theory of operator-semi-groups says that under the setting the unique solvability of the equation (with coefficient) is guaranteed. In fact, given an initial value u(0) = x in X, a unique solution of the initial-value problem can be written as u(t) = exp(-tνA)x, where {exp(-tνA)} is the analytic contraction semigroup generated by -νA. In identification problem we specify the coefficient ν by some additional information besides the unique existence of solutions. Measuring the norm ρ=||exp(-TνA)x|| of the final value u(T) as an additional information, we could have determined a unique implicit function ν=ν(x, ρ) which depends on initial-value x and norm ρ locally Lipschitz continuously.
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Report
(4 results)
Research Products
(12 results)
