Existence and uniqueness of the solution to a 3D thermoviscoelastic system
Date
2003-04-29
Authors
Bonetti, Elena
Bonfanti, Giovanna
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
3D thermoviscoelastic system, Thermomechanical modelling, Nonlinear PDE's system, Existence and uniqueness results
Citation
Bonetti, E., & Bonfanti, G. (2003). Existence and uniqueness of the solution to a 3D thermoviscoelastic system. <i>Electronic Journal of Differential Equations, 2003</i>(50), pp. 1-15.
Rights
Attribution 4.0 International