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Existence and uniqueness of the solution to a 3D thermoviscoelastic system. (English) Zbl 1034.74022
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 by 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 the initial and boundary value problem. Hence, uniqueness of the solution is proved on the whole time interval, as well as positivity of the absolute temperature.

MSC:
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74D10 Nonlinear constitutive equations for materials with memory
74A15 Thermodynamics in solid mechanics
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