Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement
In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumption...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1878 |
| _version_ | 1797572201047654400 |
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| author | Abdelkader Braik Safa M. Mirgani Eltigani I. Hassan Khaled Zennir |
| author_facet | Abdelkader Braik Safa M. Mirgani Eltigani I. Hassan Khaled Zennir |
| author_sort | Abdelkader Braik |
| collection | DOAJ |
| description | In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional. |
| first_indexed | 2024-03-10T20:51:56Z |
| format | Article |
| id | doaj.art-8e081dd15b6b41bb8ec158e242aa4309 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:56Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8e081dd15b6b41bb8ec158e242aa43092023-11-19T18:18:07ZengMDPI AGSymmetry2073-89942023-10-011510187810.3390/sym15101878Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the DisplacementAbdelkader Braik0Safa M. Mirgani1Eltigani I. Hassan2Khaled Zennir3Faculty of Sciences and Technology, University of Hassiba Ben Bouali, Chlef 02000, AlgeriaDepartment of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi ArabiaDepartment of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi ArabiaIn this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional.https://www.mdpi.com/2073-8994/15/10/1878Timoshenko-type systemstime-varying delayswell-posednessenergy decayLyapunov functionspartial differential equations |
| spellingShingle | Abdelkader Braik Safa M. Mirgani Eltigani I. Hassan Khaled Zennir Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement Symmetry Timoshenko-type systems time-varying delays well-posedness energy decay Lyapunov functions partial differential equations |
| title | Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement |
| title_full | Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement |
| title_fullStr | Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement |
| title_full_unstemmed | Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement |
| title_short | Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement |
| title_sort | well posedness and energy decay rates for a timoshenko type system with internal time varying delay in the displacement |
| topic | Timoshenko-type systems time-varying delays well-posedness energy decay Lyapunov functions partial differential equations |
| url | https://www.mdpi.com/2073-8994/15/10/1878 |
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