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Journals / Hacettepe Journal of Mathematics and Statistics / 2023 / Volume: 52 Issue: 6

Well-posedness and general energy decay of solutions for a nonlinear damping piezoelectric beams system with thermal and magnetic effects

Hassan Messaoudi(Souk Ahras University)0000-0001-9537-1661
Abdelouaheb Ardjouni(Souk Ahras University)0000-0003-0216-1265
Salah Zıtounı(Souk Ahras University)0000-0002-9949-7939
Khochemane Houssem Eddine(Ecole normale supérieure d'enseignement technologique)0000-0001-8631-514X
Pages
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Publication Date
2023-11-03
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AI Summary & Key Takeaways

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

Furthermore, our result does not depend on any relationship between system parameters.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we study the piezoelectric beams with thermal and magnetic effects in the presence of a nonlinear damping term acting on the mechanical equation.
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Key Findings & Data:First, we prove that the system is well-posed in the sense of semigroup theory.
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Conclusion & Impact:Furthermore, our result does not depend on any relationship between system parameters.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:General decay · Liapunov functional · semigroup approach

Abstract

In this article, we study the piezoelectric beams with thermal and magnetic effects in the presence of a nonlinear damping term acting on the mechanical equation. First, we prove that the system is well-posed in the sense of semigroup theory. And by constructing a suitable Liapunov functional, we show a general decay result of the solution for the system from which the polynomial and exponential decay are only special cases. Furthermore, our result does not depend on any relationship between system parameters.

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Cite This Article

Messaoudi, H., Ardjouni, A., Zıtounı, S., Eddine, K. H. (2023). Well-posedness and general energy decay of solutions for a nonlinear damping piezoelectric beams system with thermal and magnetic effects. Hacettepe Journal of Mathematics and Statistics, Volume: 52 Issue: 6. https://doi.org/10.15672/hujms.1187356

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