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研究了以下内容：（1）独特的延续定理和对具有单一磁场的施罗宾格运营商的零解决方案集估算。（2）均匀椭圆形操作员较低频谱的有限性。 （4）存在于Chern-Simons-higgs理论引起的非线性椭圆方程的非亲本解决方案。 Jimbo研究了Ginzburg-Landau方程的稳定的非稳定解决方案的存在和零集。3。田中研究了汉密尔顿系统，非元素椭圆方程的阳性溶液的Uniquness和非成分，以及构建多重倾斜溶液的构建。4。 Murata研究了抛物线方程式非负溶液的独特性。5。 Mochizuki研究了对反应扩散系统解决方案的全球存在和爆炸。6。 Ishii研究了Hypersurface的动力学和Hamilton-Jacobi方程的均匀化7。 Sakai研究了Hale-Shaw的流动，因为初始域有一个角落。

项目成果

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。

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。

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。”