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<p>In this paper, we study the long-time dynamics of the Lamé equation with strong damping and varying coefficient in unbounded domain. Combining with standard Galerkin approximation method, we first establish the global well-posedness of problem by employing the truncation function and tail estimates methods. Additionally, we demonstrate the existence and regularity of pullback attractors through the contractive function method and verify that the system exhibits quasi-stability, thereby proving the existence of pullback exponential attractors. Finally, we prove there exists a unique family of Borel invariant probability measures which is supported by the pullback attractors.</p>

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Pullback Dynamics and Invariant Measure for the Dissipative Non-Autonomous Lamé System in Unbounded Domain

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Yuming Qin,
  • Huite Jiang

摘要

In this paper, we study the long-time dynamics of the Lamé equation with strong damping and varying coefficient in unbounded domain. Combining with standard Galerkin approximation method, we first establish the global well-posedness of problem by employing the truncation function and tail estimates methods. Additionally, we demonstrate the existence and regularity of pullback attractors through the contractive function method and verify that the system exhibits quasi-stability, thereby proving the existence of pullback exponential attractors. Finally, we prove there exists a unique family of Borel invariant probability measures which is supported by the pullback attractors.