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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

Well-posedness and exponential stability of a thermoelastic-Bresse system with second sound and delay

Gang Li
Yue Luan
Wenjun Liu
Pages
523–538
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We prove that the system is well-posed by using the semigroup method, and show, using the multiplier method, that the dissipation induced by the heat is strong enough to exponentially stabilize the system in the presence of a “small" delay when the stable number is zero.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider a one-dimensional thermoelastic-Bresse system with a delay term, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacement.
📊
Key Findings & Data:In this paper, we consider a one-dimensional thermoelastic-Bresse system with a delay term, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacement.
💡
Conclusion & Impact:We prove that the system is well-posed by using the semigroup method, and show, using the multiplier method, that the dissipation induced by the heat is strong enough to exponentially stabilize the system in the presence of a “small" delay when the stable number is zero.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:thermoelastic-Bresse system · second sound · exponential decay

Abstract

In this paper, we consider a one-dimensional thermoelastic-Bresse system with a delay term, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacement. We prove that the system is well-posed by using the semigroup method, and show, using the multiplier method, that the dissipation induced by the heat is strong enough to exponentially stabilize the system in the presence of a “small" delay when the stable number is zero.

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Cite This Article

Li, G., Luan, Y., Liu, W. (2022). Well-posedness and exponential stability of a thermoelastic-Bresse system with second sound and delay. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 523–538. https://ajindex.com/articles/529559

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