Study of the structure of solutions to Variational Problems, Inverse Problems and Partial Differential Equations

1.仓田研究的存在性和定性性质的最佳解决方案的几个优化问题的非线性椭圆边值问题所产生的数学生物学和非线性热传导现象。Kurata还证明了具有Allee效应的人口增长模型的多重稳定斑图的存在性，非线性Schroedindinger方程最小能量解的对称破缺现象，以及二维非线性Schroedinger方程带涡径向解的渐近分布.研究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边界样条函数. Sakai研究了Hele-Shaw自由边界问题在初始数据具有尖点的情况下，得到了描述典型现象的充分条件.矶崎健三发现了双曲几何与反问题之间的关系。他还研究了具有不连续夹杂物的逆电导率问题，并找到了一种检测不连续性的数值算法。5.金宝继续他的研究解决方案结构的研究金斯堡-朗道方程产生的超导在异质环境下。他还研究了与麦克斯韦方程相关的椭圆算子的谱，证明了特征值的特征，并利用弱形式证明了一个扰动公式。Tanaka研究了非线性椭圆奇异摄动问题解的集中现象和解的聚集现象。特别是构造了非线性薛定谔方程的高频解和一个相变问题的多簇高能解。

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.