Electron. J. Diff. Eqns., Vol. 2003(2003), No. 50, pp. 1-15.

Existence and uniqueness of the solution to a 3D thermoviscoelastic system

Elena Bonetti & Giovanna Bonfanti

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.

Submitted December 9, 2002. Published April 29, 2003.
Math Subject Classifications: 74D10, 35K60, 74A15.
Key Words: 3D thermoviscoelastic system, thermomechanical modelling, nonlinear PDE's system, existence and uniqueness results

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Elena Bonetti
Dipartimento di Matematica
"F. Casorati", Universita di Pavia
Via Ferrata 1, 27100 Pavia, Italy
email: bonetti@dimat.unipv.it
Giovanna Bonfanti
Dipartimento di Matematica
Universita di Brescia
Via Branze 38, 25123 Brescia, Italy
email: bonfanti@ing.unibs.it

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