Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction
In this article we consider a mathematical model that describes the quasi-static process of contact between a thermo-electro-viscoelastic body and a conductive foundation. The constitutive law is assumed to be linear thermo-electro-elastic and the process is quasistatic. The contact is modelled...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/05/abstr.html |
| _version_ | 1818652379884552192 |
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| author | El-Hassan Essoufi Mohammed Alaoui Mustapha Bouallala |
| author_facet | El-Hassan Essoufi Mohammed Alaoui Mustapha Bouallala |
| author_sort | El-Hassan Essoufi |
| collection | DOAJ |
| description | In this article we consider a mathematical model that describes the
quasi-static process of contact between a thermo-electro-viscoelastic
body and a conductive foundation. The constitutive law is assumed to
be linear thermo-electro-elastic and the process is quasistatic.
The contact is modelled with a Signiorini's condition and the friction
with Tresca's law. The boundary conditions of the electric field and
thermal conductivity are assumed to be non linear. First, we establish
the existence and uniqueness result of the weak solution of the model.
The proofs are based on arguments of time-dependent variational inequalities,
Galerkin's method and fixed point theorem. Also we study a associated
penalized problem. Then we prove its unique solvability as well as the
convergence of its solution to the solution of the original problem,
as the penalization parameter tends to zero. |
| first_indexed | 2024-12-17T02:21:05Z |
| format | Article |
| id | doaj.art-8748fd645e34416f822ada926dc98970 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-17T02:21:05Z |
| publishDate | 2019-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8748fd645e34416f822ada926dc989702022-12-21T22:07:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-01-01201905,121Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's frictionEl-Hassan Essoufi0Mohammed Alaoui1Mustapha Bouallala2 Univ. Hassan 1, 26000 Settat, Morocco Univ. Hassan 1, 26000 Settat, Morocco Univ. Hassan 1, 26000 Settat, Morocco In this article we consider a mathematical model that describes the quasi-static process of contact between a thermo-electro-viscoelastic body and a conductive foundation. The constitutive law is assumed to be linear thermo-electro-elastic and the process is quasistatic. The contact is modelled with a Signiorini's condition and the friction with Tresca's law. The boundary conditions of the electric field and thermal conductivity are assumed to be non linear. First, we establish the existence and uniqueness result of the weak solution of the model. The proofs are based on arguments of time-dependent variational inequalities, Galerkin's method and fixed point theorem. Also we study a associated penalized problem. Then we prove its unique solvability as well as the convergence of its solution to the solution of the original problem, as the penalization parameter tends to zero.http://ejde.math.txstate.edu/Volumes/2019/05/abstr.htmlThermo-piezo-electricTresca's frictionSignorini's conditionvariational inequalityBanach fixed pointFaedo-Galerkin methodcompactness methodpenalty method |
| spellingShingle | El-Hassan Essoufi Mohammed Alaoui Mustapha Bouallala Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction Electronic Journal of Differential Equations Thermo-piezo-electric Tresca's friction Signorini's condition variational inequality Banach fixed point Faedo-Galerkin method compactness method penalty method |
| title | Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction |
| title_full | Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction |
| title_fullStr | Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction |
| title_full_unstemmed | Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction |
| title_short | Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction |
| title_sort | quasistatic thermo electro viscoelastic contact problem with signorini and tresca s friction |
| topic | Thermo-piezo-electric Tresca's friction Signorini's condition variational inequality Banach fixed point Faedo-Galerkin method compactness method penalty method |
| url | http://ejde.math.txstate.edu/Volumes/2019/05/abstr.html |
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