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<p>We study stability and robustness of global attractors for parabolic inclusions subjected to external disturbances entering through the boundary conditions. To this end we develop an approach consisting in investigation of a suitable family of non-autonomous semiprocesses possessing a uniform attractor, which depends on disturbances. Based on the property of its upper semicontinuity, we establish conditions guaranteeing the asymptotic gain property for the global attractor of the unperturbed system w.r.t. disturbances.</p>

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Robust Stability of Global Attractors for Parabolic Inclusion w.r.t. Boundary Disturbances

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Sergey Dashkovskiy,
  • Oleksiy Kapustyan,
  • Anna Krasnieieva

摘要

We study stability and robustness of global attractors for parabolic inclusions subjected to external disturbances entering through the boundary conditions. To this end we develop an approach consisting in investigation of a suitable family of non-autonomous semiprocesses possessing a uniform attractor, which depends on disturbances. Based on the property of its upper semicontinuity, we establish conditions guaranteeing the asymptotic gain property for the global attractor of the unperturbed system w.r.t. disturbances.