Study of Solutions to Partial Differential Equations, Variational problems and Inverse. Problems

偏微分方程、变分问题和逆问题的解的研究。

基本信息

  • 批准号:
    11640175
  • 负责人:
  • 金额:
    $ 1.47万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    1999
  • 资助国家:
    日本
  • 起止时间:
    1999 至 2000
  • 项目状态:
    已结题

项目摘要

1. Kurata studied the following :(1) estimates of the second and third derivatives of fundamental solutions to magnetic Schrodinger operators with non-smooth potentials and the Calderon-Zygmund property of certain operators.(2) estimates of the heat kernel of magnetic Schrodinger operators.(3) exiestence and further properties of the optimal configuration to several optimization problems for the first Dirichlet eigenvale. Especially, we find a symmetry-breaking pheneomena of the optimal configuration for certain symmetric domains. We also studied the regularity of the free boundary associated with the optimal configuration.2. Jimbo studied the non-existence of stable non-constant solution to Ginzburg-Landau equation with magnetic effect.3. Tanaka studied discontinuous phenomena for solutions under the perturbation to nonlinear ellitic equation -Δu+u=u^p.4. Murata studied the structure of positive solutions to elliptic and parabolic equations of second order on non-compact Riemannian manifolds.5. Mochizuki studied the blow-up and the asymptotic behavior of solutions to KPP equation and inverse spectrum problem for Sturm-Liouville operator by interior datas.6. Ishii showed the convergence of geometric approximation method for the Gauss curvature flow.7. Sakai studied the condition of the existence of a measure which has a fine support and makes the same potential outside the polygon in two-dimensional case.
1.仓田研究了以下问题:(1)具有非光滑位势的磁薛定谔算子基本解的二阶和三阶导数的估计以及某些算子的Calderon-Zygmund性质。(2)磁薛定谔算子热核的估计。(3)讨论了第一Dirichlet特征值的几个优化问题的最优配置的存在性及其性质。特别是,我们发现某些对称域的最佳配置存在对称破缺现象。我们还研究了与最优构型相关的自由边界的正则性. Jimbo研究了具有磁效应的Ginzburg-Landau方程稳定的非常数解的不存在性. Tanaka研究了非线性椭圆型方程-Δu+u= u ^p.4在扰动下解的不连续现象.村田研究了非紧黎曼流形上二阶椭圆型和抛物型方程正解的结构. Mochizuki利用内点法研究了KPP方程解的爆破和渐近性态以及Sturm-Liouville算子的逆谱问题.石井证明了高斯曲率流几何逼近方法的收敛性. Sakai研究了在二维情况下,在多边形外有一个细支集且势相等的测度存在的条件。

项目成果

期刊论文数量(49)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Hitoshi Ishii: "Gauss curvature flow and its application."Gakuto Internat.Ser.Math.Sci.Appl.. 14. 198-206 (2000)
石井仁:“高斯曲率流及其应用。”Gakuto Internat.Ser.Math.Sci.Appl.. 14. 198-206 (2000)
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S.Jimbo(with J.Zhai): "Domain perturbation method and local minimizes to Ginzburg-Landau functional with magnetic field"to appear in Abst.Appl.Anal..
S.Jimbo(与J.Zhai):“域扰动方法和局部最小化到Ginzburg-Landau泛函磁场”出现在Abst.Appl.Anal..
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    0
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Kunio Hidano: "Scatterning and self-similar solutions for the nonlinear wave equation"to appear in Diff.and Integral Eq..
Kunio Hidano:“非线性波动方程的散射和自相似解”出现在 Diff.and Integral Eq. 中。
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K.Kurata: "A Remark on finiteness of the Lower Spectrum of uniformly elliptic oparators with singular potentilas"Integral Eq. and Operator Theory. 36. 212-219 (2000)
K.Kurata:“关于具有奇异势能的均匀椭圆算子的下谱的有限性的评论”积分方程。
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    0
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H.Ishii (with S.Koike): "On ε-optimal controls for state constraint problems."Ann.Inst.H.Poincare Anal. Non Lineaire. 17. 473-502 (2000)
H.Ishii(与 S.Koike):“关于状态约束问题的 ε 最优控制”。Ann.Inst.H.Poincare Anal 17. 473-502 (2000)。
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KURATA Kazuhiro其他文献

KURATA Kazuhiro的其他文献

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{{ truncateString('KURATA Kazuhiro', 18)}}的其他基金

Study on variational problems, optimization problems and nonlinear partial differential equations
变分问题、优化问题和非线性偏微分方程研究
  • 批准号:
    16K05240
  • 财政年份:
    2016
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study on variational problems, optimization problems and nonlinear partial differential equations
变分问题、优化问题和非线性偏微分方程研究
  • 批准号:
    25400180
  • 财政年份:
    2013
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study of structures of solutions to variational problems, optimization problems and nonlinear partial differential equations
变分问题、优化问题和非线性偏微分方程解的结构研究
  • 批准号:
    22540203
  • 财政年份:
    2010
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study of the structure of solutions to variational problems, optimization problems, linear and nonlinear partial differential equations
研究变分问题、优化问题、线性和非线性偏微分方程的解结构
  • 批准号:
    18540191
  • 财政年份:
    2006
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study of the structure of solutions to Variational Problems, Inverse Problems and Partial Differential Equations
变分问题、反问题和偏微分方程解的结构研究
  • 批准号:
    15540177
  • 财政年份:
    2003
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study of Solutions to Partial Differential Equations, Variational Problems and Inverse Problems
偏微分方程、变分问题和反问题解的研究
  • 批准号:
    13640183
  • 财政年份:
    2001
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Study of Harmonic Analysis, Solutions to Variational Problems and Partial Differential Equa
调和分析、变分问题的解法和偏微分方程的研究
  • 批准号:
    09640208
  • 财政年份:
    1997
  • 资助金额:
    $ 1.47万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

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Degenerate Diffusions and Related Heat Kernel Estimates
简并扩散和相关的热核估计
  • 批准号:
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  • 财政年份:
    2019
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  • 批准号:
    1255574
  • 财政年份:
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    2013
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新一代金融工程中的热核方法
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    25285102
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    $ 1.47万
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黎曼流形和泊松核、热核的 Fisher 信息几何
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  • 财政年份:
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热核技术在对称空间商和图 Zeta 函数中的应用
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