Existence and uniqueness of the solution to a 3D thermoviscoelastic system
Southwest Texas State University, Department of Mathematics
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.
3D thermoviscoelastic system, Thermomechanical modelling, Nonlinear PDE's system, Existence and uniqueness results
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.
Attribution 4.0 International