Qualitative behavior of a class of stochastic parabolic PDES with dynamical boundary conditions

被引:0
|
作者
Chueshov, Igor [1 ]
Schmalfuss, Bjoern
机构
[1] Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine
[2] Univ Paderborn, Math Inst, D-33098 Paderborn, Germany
关键词
stochastic PDE; dynamical boundary conditions; random dynamical systems; pullback attractor; monotonicity;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider non-linear parabolic stochastic partial differential equations with dynamical boundary conditions and with a noise which acts in the domain but also on the boundary and is presented by the temporal generalized derivative of an infinite dimensional Wiener process. We prove that solutions to this stochastic partial differential equation generate a random dynamical system. Under additional conditions we show that this system is monotone. Our main result states the existence of a compact global (pullback) attractor.
引用
收藏
页码:315 / 338
页数:24
相关论文
共 50 条
  • [41] Constructive finite-dimensional boundary control of stochastic 1D parabolic PDEs
    Wang, Pengfei
    Katz, Rami
    Fridman, Emilia
    AUTOMATICA, 2023, 148
  • [42] A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions
    Ruggeri, Fabrizio
    Sawlan, Zaid
    Scavino, Marco
    Tempone, Raul
    BAYESIAN ANALYSIS, 2017, 12 (02): : 407 - 433
  • [43] Null Controllability for Stochastic Parabolic Equations with Dynamic Boundary Conditions
    Mahmoud Baroun
    Said Boulite
    Abdellatif Elgrou
    Lahcen Maniar
    Journal of Dynamical and Control Systems, 2023, 29 : 1727 - 1756
  • [44] Constructive finite-dimensional observer-based boundary control of stochastic parabolic PDEs
    Wang, Pengfei
    Katz, Rami
    Fridman, Emilia
    2022 AMERICAN CONTROL CONFERENCE, ACC, 2022, : 1667 - 1672
  • [45] Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions
    Mierczynski, J
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 209 (01) : 47 - 59
  • [46] Null Controllability for Stochastic Parabolic Equations with Dynamic Boundary Conditions
    Baroun, Mahmoud
    Boulite, Said
    Elgrou, Abdellatif
    Maniar, Lahcen
    JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2023, 29 (04) : 1727 - 1756
  • [47] A NOTE ON THE EXTENSION OF THE TSCHEBYSCHEV METHOD TO QUASILINEAR PARABOLIC PDES WITH MIXED BOUNDARY-CONDITIONS
    BERZINS, M
    DEW, PM
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1980, 8 (03) : 249 - 263
  • [48] Robust boundary conditions for stochastic incompletely parabolic systems of equations
    Wahlsten, Markus
    Nordstrom, Jan
    JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 371 : 192 - 213
  • [49] Weak formulation of stochastic parabolic systems with subdifferential boundary conditions
    Ishikawa, M
    ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE, 1995, 78 (08): : 75 - 84
  • [50] NULL CONTROLLABILITY FOR STOCHASTIC PARABOLIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS
    Boulite, Said
    Elgrou, Abdellatif
    Maniar, Lahcen
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2025,