On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

Daoyuan FANG; Linzi ZHANG; Ting ZHANG

首页> 中文期刊> 《数学年刊B辑（英文版）》 >On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

摘要

The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schrdinger equations.The local and global well-posedness are proved with values in the space Σ(■n)={f∈H1(■n),|·|f∈L2 (■n)}.When the nonlinearity is focusing and L2-supercritical,the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential.Especially for the repulsive case,the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time.Thus,compared with the deterministic equation for the repulsive case,the blow-up condition is stronger on average,and depends on the regularity of the noise.If φ=0,our results coincide with the ones for the deterministic equation.

著录项

来源
《数学年刊B辑（英文版）》 |2011年第5期|711-728|共18页
作者
Daoyuan FANG; Linzi ZHANG; Ting ZHANG;
展开▼
作者单位

Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

China;

Corresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

ChinaCorresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

ChinaCorresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

ChinaCorresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

ChinaCorresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

ChinaCorresponding author. Department of Mathematics;

Zhejiang University;

Hangzhou 310027;

China;

展开▼
原文格式 PDF
正文语种 chi
中图分类非线性偏微分方程;工程模拟;
关键词
定性方程; 随机扰动; 适定性; 充分条件; 非线性; 简谐势; 排斥势; 作者;

相似文献

中文文献
外文文献

1. A Stochastic Filtering Algorithm Using Schr¨odinger Equation [J] . WU Hao-Han ,JIN Fu-Jiang ,LAI Lian-You . 自动化学报 . 2014,第10期
2. On the well-posedness for stochastic fourth-order Schrdinger equations [J] . FANG Dao-yuan ZHANG Lin-zi ZHANG Ting . 高校应用数学学报：英文版（B辑） . 2011,第3期
3. The Existence of Solutions for a Class of Schr¨odinger Equations via Morse Index Theory [J] . LI Jia-yang ,WANG Qi . 数学季刊:英文版 . 2022,第3期
4. Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem [J] . ZHANG DE-TAO . 数学研究通讯 . 2009,第5期
5. Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem [J] . ZHANG DE-TAO . 数学研究通讯 . 2009,第5期
6. Global well-posedness of fractioal Navier-Stokes equations in variable exponent function spaces [A] . Muhammad Zainul Abidin . 2020

On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

摘要

著录项

相似文献

相关主题

期刊订阅