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<p>In this paper, we study evolution equations that are perturbed at the boundary by both noise and an unbounded perturbation. First, using the theory of regular linear systems, we prove the existence of solutions to this equation. Second, we investigate the long-time behavior of the solutions, such as the absolute continuity and the existence of an invariant measure.</p>

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Impact of mixed boundary conditions on stochastic equations with noise at the boundary

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月21日

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  • M. Fkirine,
  • S. Hadd,
  • A. Rhandi

摘要

In this paper, we study evolution equations that are perturbed at the boundary by both noise and an unbounded perturbation. First, using the theory of regular linear systems, we prove the existence of solutions to this equation. Second, we investigate the long-time behavior of the solutions, such as the absolute continuity and the existence of an invariant measure.