Acta mathematica scientia,Series B ›› 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
  • 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).

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

CLC Number: 

  • 37L40
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