权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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

基本信息

批准号：
15540177
负责人：
KURATA Kazuhiro
金额：
$ 2.18万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

1. Kurata studied the existence and qualitative properties of optimal solutions to several optimization problems for nonlinear elliptic boundary value problems arising in mathematical biology and nonlinear heat conduction phenomena. Kurata also proved the existence of multiple stable patterns in population growth model with Allee effect, symmetry breaking phenomena of the least energuy solution to nonlinear Schroedindger equation and asymptotic profile of radial solution with vortex to 2-dimensional nonlinear Schroedinger equation.2. Okada studied numerial simulation and numerical analysis of nonlinear paratial differential equations. Especially, he constructed boundary spline function by using Newton extrapolation polynomials.3. Sakai studied Hele-Shaw free boundary problem in the case that initial data has a cusp and found sufficient conditions to specify the typical pheneomena.4. Isozaki discovered the relationship between the hyperbolic geometry and inverse problem. He also studied the inverse conductivity problem with discontinuous inclusions and found a numerical algorithm to detect discontinuities.5. Jimbo continued his research on the study of solution structure of the Ginzburg-Landau equation arising in superconductivity under heterogeneous environments. He also studied the spectrum of elliptic operator associated with the Maxwell equation and proved characterization of eigenvalues and proved a perturbation formula by using weak forms.6. Tanaka studied concentration phenomena of solutions and clustered solutions for nonlinear elliptic singular perturbation problems. Especially, he constructed high frequency solution to nonlinear Schroedinger equations and multi-clustered high energySolutions to a phase transition prolem.

1. Kurata研究了数学生物学和非线性热传导现象中非线性椭圆边值问题的若干优化问题的最优解的存在性和定性性质。Kurata还证明了具有Allee效应的种群增长模型中存在多重稳定模式、非线性薛定谔方程最小能量解的对称性破缺现象和二维非线性薛定谔方程径向解带涡旋的渐近剖面。冈田研究了非线性偏微分方程的数值模拟和数值分析。特别是利用牛顿外推多项式构造了边界样条函数。3 . Sakai研究了初始数据有尖点情况下的Hele-Shaw自由边界问题，并找到了描述典型现象的充分条件。矶崎发现了双曲几何和逆问题之间的关系。他还研究了不连续夹杂的反电导率问题，并发现了一种检测不连续夹杂的数值算法。Jimbo继续研究了非均相环境下超导金兹堡-朗道方程的解结构。他还研究了与麦克斯韦方程相关的椭圆算子谱，证明了特征值的表征，并用弱形式证明了一个微扰公式。Tanaka研究了非线性椭圆型奇异摄动问题解的集中现象和聚类解。特别是，他构造了非线性薛定谔方程的高频解和相变问题的多簇高能解。