Variational Solution of Stochastic Schrodinger Equations With Power-Type Nonlinearity

被引：8

作者：

Keller, Diana ^{[1
]}

Lisei, Hannelore ^{[2
]}

机构：

[1] Univ Halle Wittenberg, Inst Math, Fac Nat Sci 2, D-06099 Halle, Saale, Germany

[2] Univ Babes Bolyai, Fac Math & Comp Sci, R-3400 Cluj Napoca, Romania

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2015年 / 33卷 / 04期

关键词：

Stochastic nonlinear Schrodinger equation; Power-type nonlinearity; Multiplicative noise; Variational solution; Galerkin method; 60H15; 35Q55; MULTIPLICATIVE NOISE; CLASSICAL-SOLUTIONS; CAUCHY-PROBLEM; DRIVEN;

D O I：

10.1080/07362994.2015.1029133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate a Schrodinger problem with multiplicative Gaussian noise term and power-type nonlinearity on a bounded one-dimensional domain. In order to prove the existence and uniqueness of the variational solution, a further process will be introduced which allows to transform the stochastic nonlinear Schrodinger problem into a pathwise one. Galerkin approximations and compact embedding results are used.

引用

页码：653 / 672

页数：20

共 36 条

[21]

Ito K., 2002, Series on Advances in Mathematics for Applied Sciences, V61

[22] Existence and uniqueness of global solutions of on R2 [J].

Jiu Q. ;

Liu J. .

Acta Mathematicae Applicatae Sinica, 1997, 13 (4) :414-424

[23]

Ladyenskaja O. A., 1968, Translations of Mathematical Monographs, V23

[24] Stabilization of solitons of the multidimensional nonlinear Schrodinger equation:: matter-wave breathers [J].

Montesinos, GD ;

Pérez-García, VM ;

Torres, PJ .

PHYSICA D-NONLINEAR PHENOMENA, 2004, 191 (3-4) :193-210

[25] Basic properties of nonlinear stochastic Schrodinger equations driven by Brownian motions [J].

Mora, Carlos M. ;

Rebolledo, Rolando .

ANNALS OF APPLIED PROBABILITY, 2008, 18 (02) :591-619

[26] Regularity of solutions to linear stochastic Schrodinger equations [J].

Mora, Carlos M. ;

Rebolledo, Rolando .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2007, 10 (02) :237-259

[27] TIME-DEPENDENT NON-LINEAR SCHRODINGER EQUATIONS [J].

PECHER, H ;

WAHL, WV .

MANUSCRIPTA MATHEMATICA, 1979, 27 (02) :125-157

[28] A note on stochastic Schrodinger equations with fractional multiplicative noise [J].

Pinaud, Olivier .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (04) :1467-1491

[29] LOCAL EXACT CONTROLLABILITY AND STABILIZABILITY OF THE NONLINEAR SCHRODINGER EQUATION ON A BOUNDED INTERVAL [J].

Rosier, Lionel ;

Zhang, Bing-Yu .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) :972-992

[30] The nonlinear Schrodinger equation with combined power-type nonlinearities [J].

Tao, Terence ;

Visan, Monica ;

Zhang, Xiaoyi .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1281-1343

← 1 2 3 4 →