Analysis of the thermoviscoelastic Timoshenko system with diffusion effect
This paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and viscoelastic effects. First, by the C0-semigroup theory, we prove the well posedness of the considered problem with Dirichlet boundary conditions. An exponential decay is obtained by construction of the Lyapuno...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818121000826 |
| _version_ | 1818572827154972672 |
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| author | M. Elhindi T. EL Arwadi |
| author_facet | M. Elhindi T. EL Arwadi |
| author_sort | M. Elhindi |
| collection | DOAJ |
| description | This paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and viscoelastic effects. First, by the C0-semigroup theory, we prove the well posedness of the considered problem with Dirichlet boundary conditions. An exponential decay is obtained by construction of the Lyapunov functional. Finally, a numerical study is done based on P1-finite element approximation for space discretization and implicit Euler scheme for time discretization, where we study the stability of the scheme, analysis of the error and obtained some numerical simulations. |
| first_indexed | 2024-12-15T00:02:50Z |
| format | Article |
| id | doaj.art-c9f76d215be94450a4649a1efb783793 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-12-15T00:02:50Z |
| publishDate | 2021-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-c9f76d215be94450a4649a1efb7837932022-12-21T22:42:50ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812021-12-014100156Analysis of the thermoviscoelastic Timoshenko system with diffusion effectM. Elhindi0T. 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, LebanonThis paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and viscoelastic effects. First, by the C0-semigroup theory, we prove the well posedness of the considered problem with Dirichlet boundary conditions. An exponential decay is obtained by construction of the Lyapunov functional. Finally, a numerical study is done based on P1-finite element approximation for space discretization and implicit Euler scheme for time discretization, where we study the stability of the scheme, analysis of the error and obtained some numerical simulations.http://www.sciencedirect.com/science/article/pii/S2666818121000826Timoshenko type systemsThermodiffusion effectsWell-posednessStabilityNumerical resultsError |
| spellingShingle | M. Elhindi T. EL Arwadi Analysis of the thermoviscoelastic Timoshenko system with diffusion effect Partial Differential Equations in Applied Mathematics Timoshenko type systems Thermodiffusion effects Well-posedness Stability Numerical results Error |
| title | Analysis of the thermoviscoelastic Timoshenko system with diffusion effect |
| title_full | Analysis of the thermoviscoelastic Timoshenko system with diffusion effect |
| title_fullStr | Analysis of the thermoviscoelastic Timoshenko system with diffusion effect |
| title_full_unstemmed | Analysis of the thermoviscoelastic Timoshenko system with diffusion effect |
| title_short | Analysis of the thermoviscoelastic Timoshenko system with diffusion effect |
| title_sort | analysis of the thermoviscoelastic timoshenko system with diffusion effect |
| topic | Timoshenko type systems Thermodiffusion effects Well-posedness Stability Numerical results Error |
| url | http://www.sciencedirect.com/science/article/pii/S2666818121000826 |
| work_keys_str_mv | AT melhindi analysisofthethermoviscoelastictimoshenkosystemwithdiffusioneffect AT telarwadi analysisofthethermoviscoelastictimoshenkosystemwithdiffusioneffect |