Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type
In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurti...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1615178 |
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| author | Mohammed M. Al-Gharabli Shadi Al-Omari Adel M. Al-Mahdi |
| author_facet | Mohammed M. Al-Gharabli Shadi Al-Omari Adel M. Al-Mahdi |
| author_sort | Mohammed M. Al-Gharabli |
| collection | DOAJ |
| description | In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations. |
| format | Article |
| id | doaj-art-b84ffd4204364aff9f34a3bae6c40a1c |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b84ffd4204364aff9f34a3bae6c40a1c2025-02-03T05:57:03ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1615178Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent TypeMohammed M. Al-Gharabli0Shadi Al-Omari1Adel M. Al-Mahdi2The Preparatory Year ProgramThe Preparatory Year ProgramThe Preparatory Year ProgramIn this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations.http://dx.doi.org/10.1155/2024/1615178 |
| spellingShingle | Mohammed M. Al-Gharabli Shadi Al-Omari Adel M. Al-Mahdi Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type Journal of Mathematics |
| title | Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type |
| title_full | Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type |
| title_fullStr | Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type |
| title_full_unstemmed | Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type |
| title_short | Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type |
| title_sort | stabilization of a rao nakra sandwich beam system by coleman gurtin s thermal law and nonlinear damping of variable exponent type |
| url | http://dx.doi.org/10.1155/2024/1615178 |
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