A stochastic nonlinear Schrodinger equation with multiplicative noise

被引：139
作者：
de Bouard, A
Debussche, A
机构：
[1] Univ Paris 11, Anal Numer Lab, F-91405 Orsay, France
[2] CNRS, EDP, F-91405 Orsay, France
[3] Univ Paris Sud, F-91405 Orsay, France
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1999年 / 205卷 / 01期
关键词：
D O I：
10.1007/s002200050672
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study a conservative stochastic nonlinear Schrodinger equation with a multiplicative noise. We show the global existence and uniqueness of square integrable solutions for subcritical nonlinearities, the critical exponent being the same, in dimension 1 or 2, as the critical exponent of the deterministic equation.
引用
收藏
页码：161 / 181
页数：21
相关论文
共 11 条
[1]  
[Anonymous], 1992, ENCY MATH ITS APPL
[2]   TEMPERATURE EFFECTS IN A NONLINEAR MODEL OF MONOLAYER SCHEIBE AGGREGATES [J].
BANG, O ;
CHRISTIANSEN, PL ;
IF, F ;
RASMUSSEN, KO ;
GAIDIDEI, YB .
PHYSICAL REVIEW E, 1994, 49 (05) :4627-4636
[3]  
Bang O., 1995, Applicable Analysis, V57, P3, DOI 10.1080/00036819508840335
[4]  
Brzeniak Z., 1997, Stoch. Stoch. Rep, V61, P245, DOI [10.1080/17442509708834122, DOI 10.1080/17442509708834122]
[5]  
BRZEZNIAK Z, IN PRESS STUDIA MATH
[6]  
CAZENAVE T, 1993, TEXTOS METODOS MATEM, V26
[7]   THE TEMPERATURE-DEPENDENT COLLAPSE REGIME IN A NONLINEAR DYNAMICAL MODEL OF SCHEIBE AGGREGATES [J].
CHRISTIANSEN, PL ;
RASMUSSEN, KO ;
BANG, O ;
GAIDIDEI, YB .
PHYSICA D, 1995, 87 (1-4) :321-324
[8]  
FIBICH G, 1997, SELF FOCUSING PERTUR
[9]   THE GLOBAL CAUCHY-PROBLEM FOR THE NON-LINEAR SCHRODINGER-EQUATION REVISITED [J].
GINIBRE, J ;
VELO, G .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1985, 2 (04) :309-327
[10]   THE INFLUENCE OF NOISE ON CRITICAL COLLAPSE IN THE NONLINEAR SCHRODINGER-EQUATION [J].
RASMUSSEN, KO ;
GAIDIDEI, YB ;
BANG, O ;
CHRISTIANSEN, PL .
PHYSICS LETTERS A, 1995, 204 (02) :121-127
12