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<p>We explore a coupled system defined on a rectangular domain with degenerate parabolic part. The model combines a wave equation and a heat equation, connected through natural transmission conditions. Our focus is on analyzing the stability of this system under Dirichlet boundary conditions. We show that when the degeneracy is relatively mild and the system’s associated semigroup exhibits polynomial stability. This enables us able to derive precise decay rates. Notably, our results not only extend previous findings but also offer improvements in certain aspects, especially when compared to known results in both one- and two-dimensional cases.</p>

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Decay estimates for semigroups associated with interactions involving degeneracy on a rectangular surface

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Ammar Moulahi

摘要

We explore a coupled system defined on a rectangular domain with degenerate parabolic part. The model combines a wave equation and a heat equation, connected through natural transmission conditions. Our focus is on analyzing the stability of this system under Dirichlet boundary conditions. We show that when the degeneracy is relatively mild and the system’s associated semigroup exhibits polynomial stability. This enables us able to derive precise decay rates. Notably, our results not only extend previous findings but also offer improvements in certain aspects, especially when compared to known results in both one- and two-dimensional cases.