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We study the long-time asymptotic behaviour of a topologically non-trivial network of wave and heat equations. By analysing the simpler wave and the heat networks separately, and then applying recent results for abstract coupled systems, we establish energy decay at the rate \(t^{-4}\) as \(t\rightarrow \infty \) for all classical solutions.

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Polynomial Stability of a Coupled Wave-Heat Network

  • 会议论文

  • 发表日期：

    2026年

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  • Lassi Paunonen,
  • David Seifert

摘要

We study the long-time asymptotic behaviour of a topologically non-trivial network of wave and heat equations. By analysing the simpler wave and the heat networks separately, and then applying recent results for abstract coupled systems, we establish energy decay at the rate \(t^{-4}\) as \(t\rightarrow \infty \) for all classical solutions.