Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms
This paper is concerned with the asymptotic behavior of the solution of a Timoshenko system with two nonlinear variable exponent damping terms. We prove that the system is stable under some specific conditions on the variable exponent and the equal wave speeds of propagation. We obtain exponential a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/538 |
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| author | Adel M. Al-Mahdi Mohammad M. Al-Gharabli |
| author_facet | Adel M. Al-Mahdi Mohammad M. Al-Gharabli |
| author_sort | Adel M. Al-Mahdi |
| collection | DOAJ |
| description | This paper is concerned with the asymptotic behavior of the solution of a Timoshenko system with two nonlinear variable exponent damping terms. We prove that the system is stable under some specific conditions on the variable exponent and the equal wave speeds of propagation. We obtain exponential and polynomial decay results by using the multiplier method, and we prove that one variable damping is enough to have polynomial and exponential decay. We observe that the decay is not necessarily improved if the system has two variable damping terms. Our results built on, developed and generalized some earlier results in the literature. |
| first_indexed | 2024-03-11T09:35:41Z |
| format | Article |
| id | doaj.art-8cbf8fcbce0e49748c3bca51676871f1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:35:41Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8cbf8fcbce0e49748c3bca51676871f12023-11-16T17:21:02ZengMDPI AGMathematics2227-73902023-01-0111353810.3390/math11030538Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping TermsAdel M. Al-Mahdi0Mohammad M. Al-Gharabli1The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaThe Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaThis paper is concerned with the asymptotic behavior of the solution of a Timoshenko system with two nonlinear variable exponent damping terms. We prove that the system is stable under some specific conditions on the variable exponent and the equal wave speeds of propagation. We obtain exponential and polynomial decay results by using the multiplier method, and we prove that one variable damping is enough to have polynomial and exponential decay. We observe that the decay is not necessarily improved if the system has two variable damping terms. Our results built on, developed and generalized some earlier results in the literature.https://www.mdpi.com/2227-7390/11/3/538Timoshenko systemenergy decayvariable exponentsnonlinear dampings |
| spellingShingle | Adel M. Al-Mahdi Mohammad M. Al-Gharabli Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms Mathematics Timoshenko system energy decay variable exponents nonlinear dampings |
| title | Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms |
| title_full | Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms |
| title_fullStr | Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms |
| title_full_unstemmed | Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms |
| title_short | Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms |
| title_sort | energy decay estimates of a timoshenko system with two nonlinear variable exponent damping terms |
| topic | Timoshenko system energy decay variable exponents nonlinear dampings |
| url | https://www.mdpi.com/2227-7390/11/3/538 |
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