数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (6): 2465-2484.doi: 10.1007/s10473-024-0622-0

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EXPONENTIAL CONVERGENCE FOR NONLINEAR SPDES WITH DOUBLE REFLECTING WALLS

Dengdi CHEN, Yan ZHENG   

  1. College of Sciences, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2023-04-13 修回日期:2024-05-29 发布日期:2024-12-06
  • 通讯作者: † Yan ZHENG, E-mail: yanzhengyl@163.com
  • 作者简介:Dengdi CHEN, E-mail: dengdichen@yeah.net
  • 基金资助:
    National Natural Science Foundation of China (12071480), the Scientific Research Program Funds of NUDT (22-ZZCX-016) and the Hunan Provincial Innovation Foundation for Postgraduate (CX20230003).

EXPONENTIAL CONVERGENCE FOR NONLINEAR SPDES WITH DOUBLE REFLECTING WALLS

Dengdi CHEN, Yan ZHENG   

  1. College of Sciences, National University of Defense Technology, Changsha 410073, China
  • Received:2023-04-13 Revised:2024-05-29 Published:2024-12-06
  • Contact: † Yan ZHENG, E-mail: yanzhengyl@163.com
  • About author:Dengdi CHEN, E-mail: dengdichen@yeah.net
  • Supported by:
    National Natural Science Foundation of China (12071480), the Scientific Research Program Funds of NUDT (22-ZZCX-016) and the Hunan Provincial Innovation Foundation for Postgraduate (CX20230003).

摘要: The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate, multiplicative noise. We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling, in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.

关键词: stochastic partial differential equations with double reflecting walls, exponential mixing, asymptotic coupling, Girsanov transform

Abstract: The present article is devoted to nonlinear stochastic partial differential equations with double reflecting walls driven by possibly degenerate, multiplicative noise. We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure through asymptotic coupling, in which Foias-Prodi estimation and the truncation technique are crucial for the realization of the Girsanov transform.

Key words: stochastic partial differential equations with double reflecting walls, exponential mixing, asymptotic coupling, Girsanov transform

中图分类号: 

  • 37L40