MANY-FACETED ATTACK ON THE COMPLEX GINZBURG-LANDAU EQUATION

对复杂 GINZBURG-LANDAU 方程的多方面攻击

• 批准号: 17540172
• 负责人: OKAZAWA Noboru
• 金额: $ 1.31万
• 依托单位: Tokyo University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540172/
• 关键词: THE COMPLEX GINZBURG-LANDAU EQUATION; SMOOTHING EFFECT; LEBESGUE SPACE; SOBOLEV SPACE; EIGENVALUE OF LAPLACIAN; ESTIMATE OF EIGENFUNCTION; SCHROEDINGER OPERATORS; QUASI-M-ACCRETIVITY; 複素Ginzburg-Landau方程式; Laplacianの固有値問題; 定常問題; アトラクター; Agmonの

1) Initial-boundary value problems for the complex Ginzburg-Landau equation on a bounded domain is discussed when we take the initial values from the Lebesgue space L-p (p>2). As a corollary we can reformulate the result of Ginibre-Velo (1997) in which the initial values are taken from the Sobolev space H-1. In addition we can weaken the restriction on the exponents of the power of the nonlinear term if we take the initial values from H-m (m is a integer greater than or equal to 2). The stationary problems are also considered. (2) We have presented a new sufficient condition which guarantees the quasi-m-accretivity of Schroedinger operators with singular first-order coefficients. The result is regarded as an improvement of that by late Professor Tosio Kato. (3) We have obtained the estimates of the eigenfunctions e_n of the Laplace operator on a bounded domain. | (e_n) (x) | is bounded by the constant multiple of the eigenvalue to the power of N/4. This exponent with N=1 appears in the estimates of the eigenfunctions of the Schroedinger operator of the one-dimensional harmonic ocsilltor.

1）当我们从Lebesgue Space L-P（P> 2）中获取初始值时，讨论了一个有界域上复杂的Ginzburg-Landau方程的初始界值问题。作为推论，我们可以重新制定Ginibre-Velo（1997）的结果，其中最初的值是从Sobolev Space H-1中获取的。此外，如果我们从H-M中获取初始值（M是大于或等于2），则可以削弱对非线性项幂指数的限制。还考虑了固定问题。 （2）我们提出了一种新的足够条件，可以保证具有单数一阶系数的Schroedinger操作员的准M-核能。该结果被已故的Tosio Kato教授视为改进的结果。 （3）我们获得了有界域上拉普拉斯操作员的特征函数E_N的估计值。 | （e_n）（x）|由特征值的常数倍数与N/4的功率界定。该指数具有n = 1的指数出现在一维谐波Ocsilltor的Schroedinger操作员的特征函数的估计中。

项目成果

SMOOTHING EFFECT FOR THE CMPLEX GINZBURG-LANDAU EQUATION (GENERAL CASE

复数 GINZBURG-LANDAU 方程的平滑效应（一般情况）

• 发表时间: 2006
• 期刊: DYNAMICS OF CONTINUOUS, DISCRETE AND IMPULSIVE SYSTEMS(SERIES A : MATHEMATICAL ANALYSIS 13
• 作者: T.;YOKOTA AND N. OKAZAWA
• 通讯作者: YOKOTA AND N. OKAZAWA

Quasi-m-accretivity of Schroedinger operators with singular first-order coefficients

具有奇异一阶系数的薛定谔算子的拟m-累加性

• 发表时间: 2008
• 期刊: Discrete and Continuous Dynamical Systems (Special Issue)(印刷中)
• 作者: N. Okazawa;T. Yokota
• 通讯作者: T. Yokota

SEMILINEAR ELLIPTIC PROBLEMS ASSOCIATED WITH THE COMPLEX GINZBURG-LANDAU EQUATION

与复GINZBURG-LANDAU方程相关的半线性椭圆问题

• 发表时间: 2006
• 期刊: PDE AND FUNCTIONAL ANALYSIS(OPERATOR THEORY : ADVANCES AND APPLICATIONS 168
• 作者: N.;OKAZAWA
• 通讯作者: OKAZAWA

Semilinear elliptic problems associated with the complex Ginzburg-Landauequation

与复杂的 Ginzburg-Landaue 方程相关的半线性椭圆问题

• 发表时间: 2006
• 期刊: PDE and Functional Analysis Operator Theory:Advances and Applications 168
• 作者: T.;YOKOTA;N.;OKAZAWA;Noboru Okazawa;Noboru Okazawa
• 通讯作者: Noboru Okazawa

Smoothing effect and strong L^2-wellposedness in the complex Ginzburg-Landau equation

复杂 Ginzburg-Landau 方程中的平滑效应和强 L^2 适定性

• 发表时间: 2006
• 期刊: Differential Equations:Inverse and Direct Problems Lecture Notes in Pure and Applied mathematics 251
• 作者: T.;YOKOTA;N.;OKAZAWA;Noboru Okazawa
• 通讯作者: Noboru Okazawa