Geodesic
Existence and uniqueness of the solution to a 3D thermoviscoelastic system
Electronic journal of differential equations, Tome 2003 (2003)
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__a38,
     author = {Bonetti,  Elena and Bonfanti,  Giovanna},
     title = {Existence and uniqueness of the solution to a {3D} thermoviscoelastic system},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1034.74022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a38/}
}
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UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a38/
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%A Bonfanti,  Giovanna
%T Existence and uniqueness of the solution to a 3D thermoviscoelastic system
%J Electronic journal of differential equations
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%V 2003
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%F EJDE_2003__2003__a38
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__a38/