Frequency-dependent damping in the linear wave equation

Francesco Maddalena; Gianluca Orlando; Francesco Maddalena; Gianluca Orlando

doi:10.3934/nhm.2025019

Networks and Heterogeneous Media

2025, Volume 20, Issue 2: 406-427. doi: 10.3934/nhm.2025019

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Research article

Frequency-dependent damping in the linear wave equation

Francesco Maddalena ,
Gianluca Orlando ^,

Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, I–70125 Bari, Italy

Received: 05 March 2025 Revised: 22 April 2025 Accepted: 24 April 2025 Published: 06 May 2025
35L05, 35L20, 35B40

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for special choices of the damping operator. Finally, we show, in special cases, that solutions split into a dissipative and a conservative part.
- wave equation,
- frequency-dependent damping,
- well-posedness,
- energy decay
Citation: Francesco Maddalena, Gianluca Orlando. Frequency-dependent damping in the linear wave equation[J]. Networks and Heterogeneous Media, 2025, 20(2): 406-427. doi: 10.3934/nhm.2025019

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Abstract

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for special choices of the damping operator. Finally, we show, in special cases, that solutions split into a dissipative and a conservative part.

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