Inhomogeneous initial-boundary value problem for the 2Dnonlinear Schrödinger equation
Inhomogeneous initial-boundary value problem for the 2Dnonlinear Schrödinger equation
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二维非线性薛定谔方程的非齐次初边值问题
DOI：
10.1063/1.5043630
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发表时间：
2018
影响因子：
1.3
通讯作者：
E. Kaikina
中科院分区：
文献类型：
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作者：
E. Kaikina
我们考虑在右上四分之一平面上表述的非线性多维薛定谔方程的非齐次狄利克雷初始边值问题。我们研究非线性偏微分方程理论的传统重要问题，例如初始边值问题解的全局时间存在性和大时间解的渐近行为。我们也有兴趣研究狄利克雷边界数据对解的渐近行为的影响。我们获得非线性问题适定性的方法基于研究线性理论，然后使用不动点论证。为了获得多维模型的线性理论，我们提出了一种基于黎曼-希尔伯特方法和柯西型积分方程理论的通用方法。为了获得L∞中的平滑解，我们修改了基于自由薛定谔演化群分解的方法。我们考虑在右上四分之一平面上表述的非线性多维薛定谔方程的非齐次狄利克雷初始边值问题。我们研究非线性偏微分方程理论的传统重要问题，例如初始边值问题解的全局时间存在性和大时间解的渐近行为。我们也有兴趣研究狄利克雷边界数据对解的渐近行为的影响。我们获得非线性问题适定性的方法基于研究线性理论，然后使用不动点论证。为了获得多维模型的线性理论，我们提出了一种基于黎曼-希尔伯特方法和柯西型积分方程理论的通用方法。为了获得 L∞ 中的平滑解，我们修改了基于自由薛定谔演化群分解的方法。
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear multidimensional Schrodinger equation, formulated on an upper right-quarter plane. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time. Also we are interested in the study of the influence of the Dirichlet boundary data on the asymptotic behavior of solutions. Our approach to get well-posedness of nonlinear problems is based on studying a linear theory and then using the fixed point argument. To get a linear theory for the multidimensional model, we proposed a general method based on the Riemann–Hilbert approach and theory Cauchy type integral equations. To get smooth solutions in L∞, we modify a method based on the factorization for the free Schrodinger evolution group.We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear multidimensional Schrodinger equation, formulated on an upper right-quarter plane. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time. Also we are interested in the study of the influence of the Dirichlet boundary data on the asymptotic behavior of solutions. Our approach to get well-posedness of nonlinear problems is based on studying a linear theory and then using the fixed point argument. To get a linear theory for the multidimensional model, we proposed a general method based on the Riemann–Hilbert approach and theory Cauchy type integral equations. To get smooth solutions in L∞, we modify a method based on the factorization for the free Schrodinger evolution group.
带有排斥指令的非线性薛定谔方程解的尖锐渐近行为
DOI：
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发表时间：
2005
期刊：
Communications in Contemporary Mathematics Vol7・No2(To appear)
影响因子：
--
作者：
Naoyasu Kita;Tohru Ozawa
通讯作者：
Tohru Ozawa
半直线上拟微分方程的非线性理论
DOI：
--
发表时间：
2004
期刊：
影响因子：
--
作者：
Frebel;Anna; Aoki;Wako; Christlieb;Norbert; Ando;Hiroyasu; Asplund;Martin; Barklem;Paul S.; Beers;Timothy C.; Eriksson;Kjell; Fechner;Cora; Fujimoto;Masayuki Y.; Honda;Satoshi; Kajino;Toshitaka; Minezaki;Takeo; Nomoto;Ken'ichi; Norris;John ;K.Miwa et al.;T.Nakanishi;H.Sakurai;Nakao Hayashi
通讯作者：
Nakao Hayashi
半线上的本杰明-小野方程
影响因子：
1.2
作者：
M. Maejima;C.A. Tudor;N. Hayashi and E. Kaikina
通讯作者：
N. Hayashi and E. Kaikina