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
• 负责人: KURATA Kazuhiro
• 金额: $ 1.47万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640183/
• 关键词: Cahn-Hilliard energy; Chern-Simons-Higgs theory; optimization problem; first Dirichlet eigenvalue; Ginzburg-Landau equation; Martin boundary; inverse spectrum problem; Hale-Shaw flow; 変分問題; 楕円型境界値問題; Ginzburg-Landau方程式; 非線形Schrodinger方程式; スペクト

1. Kurata studied the following:(1) breakdown of the monotonicity of the minimizer to a one-dimensional Cahn-Hilliard energy with inhomogeneous weight and the existence of non-topological solution to a nonlinear elliptic equation arising from Chern-Simons-Higgs theory.(2) optimal location of a obstacle in an optimization problem for the first Dirichlet eigenvalue to Schrodinger operator.2. Jimbo studied the existence of stable vortex solutions and the non-existence of permanent current in a convex domain to Ginzburg-Landau equation with magnetic effect. Tanaka constructed solutions with complex patterns to inhomogeneous Allen-Cahn equation and nonlinear Schrodinger equation. Murata studied the structure of positive solutions to elliptic equation of skew-product type and classifies the Martin boundary and Martin kernel completely.3. Mochizuki studied the inverse spectrum problem for Dirac operator and Sturm-Liouville operator by interior datas. Sakai studied the asymptotic behavior of the moving boundary for Hale-Shaw flow when the initial region has an angle in details.

1。库拉塔研究了以下内容：（1）最小化的单调性对一维的cahn-hilliard能量，具有不均匀重量的单调性，并且存在非平衡椭圆形方程的非平衡解决方案对chern-simons-higgs理论的最佳位置而引起的非线性椭圆方程。操作员2。 Jimbo研究了稳定的涡旋溶液的存在，并且具有磁性效应的凸域中的永久电流不存在。田中构建了具有复杂模式的解决方案，旨在使Allen-Cahn方程和非线性Schrodinger方程。 Murata研究了偏斜类型椭圆方程的阳性解决方案的结构，并完全对Martin Boundare和Martin内核进行了分类。3。 Mochizuki研究了室内数据的Dirac操作员和Sturm-Liouville操作员的逆频谱问题。当初始区域的细节角度时，Sakai研究了Hale-Shaw流动边界的渐近行为。

项目成果

Mochizuki(with I.A.Shishmarev): "Large time asymptotics of small solutions to generalized Kolmogorov-Petrovskii-Piskunov equation"Funkcialai Ekvasioj. 44. 99-117 (2001)

Mochizuki（与 I.A.Shishmarev）：“广义 Kolmogorov-Petrovskii-Piskunov 方程小解的大时间渐近”Funkcialai Ekvasioj。

Kazuhiro Kurata: "Existence of non-topological solutions for a nonlinear elliptic equation arising from Chern-Simons-Higgs theory in a general background metric"Duff. Integral Equations. 14. 925-935 (2001)

Kazuhiro Kurata：“在一般背景度量中，由 Chern-Simons-Higgs 理论产生的非线性椭圆方程的非拓扑解的存在”Duff。

Kimie Nakashima: "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems"Ann. Inst, H. Poincare Anal. Non Lineaire. 20. 107-143 (2003)

Kimie Nakashima：“空间非均匀相变问题中的聚类层和边界层”Ann。

田中和永, L.Jeanjean: "A positive solution for an asymptotically linear elliptic problem on R^N autonomous at infinity"ESAIM Control Optim. Calc. Var.. 7. 597-614 (2002)

Kazunaga Tanaka，L.Jeanjean：“无穷大 R^N 自治的渐近线性椭圆问题的正解”ESAIM Control Calc。7. 597-614 (2002)

田中和永, K.Nakashima: "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems"Ann. Inst. H. Poincare Anal. Non Lineaire.. 20. 107-143 (2003)

Kazunaga Tanaka，K.Nakashima：“空间非均匀相变问题中的聚类层和边界层”Ann. H. Poincare Anal.. 20. 107-143 (2003)