Geodesic
Existence and uniqueness of the solution to a 3D thermoviscoelastic system
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 74D10, 35K60, 74A15
Keywords: 3D thermoviscoelastic system, thermomechanical modelling, nonlinear PDE's system 
@article{EJDE_2003__2003__a138,
     author = {Bonetti, Elena and Bonfanti, Giovanna},
     title = {Existence and uniqueness of the solution to a {3D} thermoviscoelastic system},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a138/}
}
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Bonetti, Elena; Bonfanti, Giovanna. Existence and uniqueness of the solution to a 3D thermoviscoelastic system. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a138/