General decay for a coupled wave problem with Lord-Shulman thermal heat law and delay

Hasan Almutairi; Hasan Almutairi

doi:10.3934/era.2026046

Electronic Research Archive

2026, Volume 34, Issue 2: 997-1016. doi: 10.3934/era.2026046

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General decay for a coupled wave problem with Lord-Shulman thermal heat law and delay

Hasan Almutairi ^,

Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 31991, Saudi Arabia

Received: 13 November 2025 Revised: 15 January 2026 Accepted: 17 January 2026 Published: 29 January 2026

This article study a coupled one-dimensional hyperbolic system with Lord-Shulman thermal heat law on the first equation, and a general weak inherent damping, along with time-dependent coefficient and time-varying delay term on the second equation. Using the multiplier method, through a suitable Lyapunov functional, we prove a general decay stability result that encompasses both exponential and polynomial decay estimates as special cases. This result extends and generalizes existing findings in the literature related to the system under study.
- general decay,
- coupled wave,
- Lord-Shulman thermal law,
- time varying coefficient and delay
Citation: Hasan Almutairi. General decay for a coupled wave problem with Lord-Shulman thermal heat law and delay[J]. Electronic Research Archive, 2026, 34(2): 997-1016. doi: 10.3934/era.2026046

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Abstract

This article study a coupled one-dimensional hyperbolic system with Lord-Shulman thermal heat law on the first equation, and a general weak inherent damping, along with time-dependent coefficient and time-varying delay term on the second equation. Using the multiplier method, through a suitable Lyapunov functional, we prove a general decay stability result that encompasses both exponential and polynomial decay estimates as special cases. This result extends and generalizes existing findings in the literature related to the system under study.

References

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