Existence and uniqueness of the solution to a 3D thermoviscoelastic system
This paper presents results on existence and uniqueness of solutions to a three-dimensional thermoviscoelastic system. The constitutive relations of the model are recovered by a free energy functional and a pseudo-potential of dissipation. Using a fixed point argument, combined with an a priori esti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/50/abstr.html |
| _version_ | 1818834316576161792 |
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| author | Elena Bonetti Giovanna Bonfanti |
| author_facet | Elena Bonetti Giovanna Bonfanti |
| author_sort | Elena Bonetti |
| collection | DOAJ |
| description | This paper presents results on existence and uniqueness of solutions to a three-dimensional thermoviscoelastic system. The constitutive relations of the model are recovered by a free energy functional and a pseudo-potential of dissipation. Using a fixed point argument, combined with an a priori estimates-passage to the limit technique, we prove a local existence result for a related initial and boundary values problem. Hence, uniqueness of the solution is proved on the whole time interval, as well as positivity of the absolute temperature. |
| first_indexed | 2024-12-19T02:32:53Z |
| format | Article |
| id | doaj.art-2677f900228c4d79968c70be08eff3da |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T02:32:53Z |
| publishDate | 2003-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2677f900228c4d79968c70be08eff3da2022-12-21T20:39:33ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-04-01200350115Existence and uniqueness of the solution to a 3D thermoviscoelastic systemElena BonettiGiovanna BonfantiThis paper presents results on existence and uniqueness of solutions to a three-dimensional thermoviscoelastic system. The constitutive relations of the model are recovered by a free energy functional and a pseudo-potential of dissipation. Using a fixed point argument, combined with an a priori estimates-passage to the limit technique, we prove a local existence result for a related initial and boundary values problem. Hence, uniqueness of the solution is proved on the whole time interval, as well as positivity of the absolute temperature.http://ejde.math.txstate.edu/Volumes/2003/50/abstr.html3D thermoviscoelastic systemthermomechanical modellingnonlinear PDE's systemexistence and uniqueness results. |
| spellingShingle | Elena Bonetti Giovanna Bonfanti Existence and uniqueness of the solution to a 3D thermoviscoelastic system Electronic Journal of Differential Equations 3D thermoviscoelastic system thermomechanical modelling nonlinear PDE's system existence and uniqueness results. |
| title | Existence and uniqueness of the solution to a 3D thermoviscoelastic system |
| title_full | Existence and uniqueness of the solution to a 3D thermoviscoelastic system |
| title_fullStr | Existence and uniqueness of the solution to a 3D thermoviscoelastic system |
| title_full_unstemmed | Existence and uniqueness of the solution to a 3D thermoviscoelastic system |
| title_short | Existence and uniqueness of the solution to a 3D thermoviscoelastic system |
| title_sort | existence and uniqueness of the solution to a 3d thermoviscoelastic system |
| topic | 3D thermoviscoelastic system thermomechanical modelling nonlinear PDE's system existence and uniqueness results. |
| url | http://ejde.math.txstate.edu/Volumes/2003/50/abstr.html |
| work_keys_str_mv | AT elenabonetti existenceanduniquenessofthesolutiontoa3dthermoviscoelasticsystem AT giovannabonfanti existenceanduniquenessofthesolutiontoa3dthermoviscoelasticsystem |