Invariant measures for stochastic nonlinear beam and wave equations

被引：62
|
作者：
Brzezniak, Zdzislaw [2 ]
Ondrejat, Martin [1 ]
Seidler, Jan [1 ]
机构：
[1] Czech Acad Sci, Inst Informat Theory & Automat, Vodarenskou Vezi 4, CZ-18208 Prague 8, Czech Republic
[2] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 05期
关键词：
EVOLUTION-EQUATIONS; WEAK SOLUTIONS; SPDES;
D O I：
10.1016/j.jde.2015.11.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Existence of an invariant measure for a stochastic extensible beam equation and for a stochastic damped wave equation with polynomial nonlinearities is proved. It is shown first that the corresponding transition semigroups map the space of all bounded sequentially weakly continuous functions on the state space into itself and then by a Lyapunov functions approach solutions bounded in probability are found. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：4157 / 4179
页数：23
相关论文
共 50 条
  • [1] Invariant Measures for Stochastic Nonlinear Schrodinger Equations
    Hong, Jialin
    Wang, Xu
    INVARIANT MEASURES FOR STOCHASTIC NONLINEAR SCHRODINGER EQUATIONS: NUMERICAL APPROXIMATIONS AND SYMPLECTIC STRUCTURES, 2019, 2251 : 63 - 79
  • [2] PERIODIC AND INVARIANT MEASURES FOR STOCHASTIC WAVE EQUATIONS
    Kim, Jong Uhn
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2004,
  • [3] INVARIANT-MEASURES FOR NONLINEAR STOCHASTIC DIFFERENTIAL-EQUATIONS
    BAXENDALE, PH
    LECTURE NOTES IN MATHEMATICS, 1991, 1486 : 123 - 140
  • [4] Numerical Invariant Measures for Damped Stochastic Nonlinear Schrodinger Equations
    Hong, Jialin
    Wang, Xu
    INVARIANT MEASURES FOR STOCHASTIC NONLINEAR SCHRODINGER EQUATIONS: NUMERICAL APPROXIMATIONS AND SYMPLECTIC STRUCTURES, 2019, 2251 : 109 - 152
  • [5] Invariant Measures for Stochastic Differential Equations
    Hong, Jialin
    Wang, Xu
    INVARIANT MEASURES FOR STOCHASTIC NONLINEAR SCHRODINGER EQUATIONS: NUMERICAL APPROXIMATIONS AND SYMPLECTIC STRUCTURES, 2019, 2251 : 31 - 61
  • [6] Invariant manifolds for stochastic wave equations
    Lu, Kening
    Schmalfuss, Bjoern
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 236 (02) : 460 - 492
  • [7] Stochastic nonlinear beam equations
    Brzezniak, Z
    Maslowski, B
    Seidler, J
    PROBABILITY THEORY AND RELATED FIELDS, 2005, 132 (01) : 119 - 149
  • [8] Stochastic nonlinear beam equations
    Zdzisław Brzeźniak
    Bohdan Maslowski
    Jan Seidler
    Probability Theory and Related Fields, 2005, 132 : 119 - 149
  • [9] Periodic measures of fractional stochastic discrete wave equations with nonlinear noise
    Li, Xintao
    She, Lianbing
    Yao, Jingjing
    DEMONSTRATIO MATHEMATICA, 2024, 57 (01)
  • [10] Invariant measures for stochastic functional differential equations
    Butkovsky, Oleg
    Scheutzow, Michael
    ELECTRONIC JOURNAL OF PROBABILITY, 2017, 22
12345