| Project/Area Number |
20540190
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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 | 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) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 関数解析 / 複素Ginzburg-Landau方程式 / 非線形Schrodinger方程式 / 逆二乗ポテンシャル / エネルギー法 / コンパクト性の方法 / Coulomb 特異性 / 楕円型作用素 / 半群の解析性 / Katoの方法 / (A)型の作用素整型族 / Schrodinger作用素 / Cauchy問題 / Stricharts評価 / 双曲型発展方程式 / Dirac方程式 / 劣微分作用素 / 単調な非線形項の場合 / 非単調な非線形項の場合 / 重複Laplacian / 非線形Schrodinger型方程式 / Linear evolution equation / Hyperboic type / The Dirac equation / Bi-Laplacian / Singular potential / Selfadjointness / m-accretivity / Holomorphic family |
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| Research Abstract |
Three main subjects in the application form are stated as follows: (A) The complex Ginzburg-Landau equation;(B) 2nd order linear parabolic equations including 1st order terms with unbounded coefficients;(C) (abstract) non-normal form evolution equations of hyperbolic type. Also, we have studied five subjects related to (A), (B) and (C): (D) The Dirac equation and linear Schrodinger equation with time-dependent potential; (E) Nonlinear Schrodinger equation with inverse-square potential; (F) The operator 2+t|x|-4as a 4thorder analog of Schrodinger operator +t|x|-2(t is a real parameter); (G) Holomorphic family of Schrodinger operator { + k V(x)} in Lp(κ is a complex parameter); (H) Analyticity of the semigroups generated by 2ndorder linear elliptic operators including 1storder terms with unbounded coefficients.
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