Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach
Numerous studies have been conducted to investigate porous systems under different damping effects. Recent research has consistently achieved the expected exponential decay of energy solutions when employing stabilization techniques that involve non-physical assumptions of equal wave velocities. In...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000050 |
| _version_ | 1797260361149186048 |
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| author | Hamza Zougheib Toufic El Arwadi |
| author_facet | Hamza Zougheib Toufic El Arwadi |
| author_sort | Hamza Zougheib |
| collection | DOAJ |
| description | Numerous studies have been conducted to investigate porous systems under different damping effects. Recent research has consistently achieved the expected exponential decay of energy solutions when employing stabilization techniques that involve non-physical assumptions of equal wave velocities. In this study, we examine a one-dimensional thermoelastic porous system within the framework of the second frequency spectrum. Remarkably, we demonstrate that exponential decay can be achieved without relying on the assumption of equal wave speeds. We consider the porous system, and we incorporated thermoelastic damping based on the Green–Naghdi law of heat conduction into our study. To begin with, we use the Faedo–Galerkin approximation method to validate the global well-posedness of the system. By utilizing a Lyapunov functional, we establish exponential stability without relying on the assumption of equal wave speed. We then introduce and analyze a numerical scheme. Finally, by assuming additional regularity of the solution, we derive a priori error estimates. |
| first_indexed | 2024-03-08T13:01:28Z |
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| id | doaj.art-ae84d5093c4c47bd96b31405070d728e |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-24T23:24:06Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
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| series | Results in Applied Mathematics |
| spelling | doaj.art-ae84d5093c4c47bd96b31405070d728e2024-03-16T05:09:09ZengElsevierResults in Applied Mathematics2590-03742024-02-0121100435Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approachHamza Zougheib0Toufic El Arwadi1Corresponding author.; Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, LebanonDepartment of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, LebanonNumerous studies have been conducted to investigate porous systems under different damping effects. Recent research has consistently achieved the expected exponential decay of energy solutions when employing stabilization techniques that involve non-physical assumptions of equal wave velocities. In this study, we examine a one-dimensional thermoelastic porous system within the framework of the second frequency spectrum. Remarkably, we demonstrate that exponential decay can be achieved without relying on the assumption of equal wave speeds. We consider the porous system, and we incorporated thermoelastic damping based on the Green–Naghdi law of heat conduction into our study. To begin with, we use the Faedo–Galerkin approximation method to validate the global well-posedness of the system. By utilizing a Lyapunov functional, we establish exponential stability without relying on the assumption of equal wave speed. We then introduce and analyze a numerical scheme. Finally, by assuming additional regularity of the solution, we derive a priori error estimates.http://www.sciencedirect.com/science/article/pii/S2590037424000050Exponential decayPorous systemThermoelasticityFinite element analysis |
| spellingShingle | Hamza Zougheib Toufic El Arwadi Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach Results in Applied Mathematics Exponential decay Porous system Thermoelasticity Finite element analysis |
| title | Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach |
| title_full | Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach |
| title_fullStr | Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach |
| title_full_unstemmed | Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach |
| title_short | Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach |
| title_sort | energy decay analysis for porous elastic system with thermoelasticity of type iii a second spectrum approach |
| topic | Exponential decay Porous system Thermoelasticity Finite element analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000050 |
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