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
• 负责人: KURATA Kazuhiro
• 金额: $ 1.41万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640208/
• 关键词: Super conductivity; Ginzburg-Landau equation; Sem-classical limit; Schrodinger operator; spectrum; elliptic equation; variational problem; singular perturbation problem; スペクトエル; Morrey空間; ハミルトン・ヤコビ方程式; 一意接続性定理; Chern-Simons-Higgs理論; スカラー曲率方程式

1. Kurata studied the following :(1) unique continuation theorem and an estimate of zero set of solutions to Schrodinger operators with singular magnetic fields.(2) finiteness of the lower spectrum of uniformly elliptic operators singular potentials.(3) Liouville type theorem for Ginzburg-Landau equation and existence and its profile of the least energy solution to nonlinear Schrodinger equation with magnetic effect.(4) existence of non-topological solution to a nonlinear elliptic equation arising from Chern-Simons-Higgs theory2. Jimbo studied existence and zero set of stable non-constant solution to Ginzburg-Landau equation.3. Tanaka studied Hamilton system, uniquness and non-degeneracy of positive solution to a nonlinea elliptic equation, and the construction of multi-bump solutions.4. Murata studied uniqueness of non-negative solution to parabolic equation.5. Mochizuki studied global existence and blow-up of solutions to reaction-diffusion systems.6. Ishii studied dynamics of hypersurfaces and homogenization of Hamilton-Jacobi equation.7. Sakai studied Hale-Shaw flow in the case that initial domain has a corner.

1. Kurata研究了以下问题：（1）具有奇异磁场的Schrodinger算子的唯一延拓定理和零解集的估计。(2)一致椭圆算子奇异势下谱的有限性。(3)Ginzburg-Landau方程的Liouville型定理和具有磁效应的非线性Schrodinger方程最小能量解的存在性及其轮廓。(4)由Chern-Simons-Higgs理论导出的一类非线性椭圆型方程非拓扑解的存在性2. Jimbo研究了Ginzburg-Landau方程稳定的非常数解的存在性和零集. Tanaka研究了汉密尔顿系统，一类非线性椭圆型方程正解的唯一性和非退化性，以及多凸解的构造. Murata研究了抛物型方程非负解的唯一性. Mochizuki研究了反应扩散方程组解的整体存在性和爆破性.石井研究了超曲面的动力学和Hamilton-Jacobi方程的均匀化. Sakai研究了初始区域有角点情况下的Hale-Shaw流。

项目成果

Kazuhiro Kurata: "A Liouville type Theorem for the Ginzburg-Landau equations with General Potentials." in an added volume to Discrete and Continuous Dynamical Systems, Edited by W.Chen, S.Hu. 17-23 (1998)

Kazuhiro Kurata：“具有一般势的 Ginzburg-Landau 方程的 Liouville 型定理。”

K.Kurata: "Local boundedness and continuity for weak solutions of -(*-ib)^2u+Vu=0" Math.Z.224. 641-653 (1997)

K.Kurata：“-(*-ib)^2u Vu=0 弱解的局部有界性和连续性”Math.Z.224。

H.Ishii(with Arisawa, Mariko): "Some properties of ergodic attractors for controlled dynamical systems." Discrete Contin. Dynam. Systems 4. no.1. 43-54 (1998)

H.Ishii（与 Arisawa、Mariko）：“受控动力系统的遍历吸引子的一些特性。”

H.Ishii(with K.Horie): "Homogenization of Hamilton-Jacobi equations on domains with small scale peri-odic structure," Indiana Univ.Math.J.47. 1011-1058 (1998)

H.Ishii（与 K.Horie）：“具有小尺度周期性结构的域上的 Hamilton-Jacobi 方程的均匀化”，Indiana Univ.Math.J.47。

K.Hidano,: "Nonlinear small data scattering for the wave equation in R^<4+1>" J.Math.Soc.Japan. 50. (1998)

K.Hidano，：“R^<4 1> 中波动方程的非线性小数据散射”J.Math.Soc.Japan。