On the forward and backward in time problems in the Kelvin–Voigt thermoviscoelastic materials

Abstract

This paper studies the uniqueness of solutions to the forward and backward in time boundary value problems associated with the Kelvin–Voigt viscoelastic model of the thermoelastic materials. For thermoviscoelastic materials with a center of symmetry, it is shown the uniqueness of solutions to the forward in time boundary value problems without any assumptions upon the thermoviscoelastic constitutive coefficients other than the symmetry properties and those induced by the dissipation inequality. While for the final boundary value problems two uniqueness theorems are presented: the first one is essentially based on the assumption that the specific heat is of negative definite sign, while the second is established in the class of displacement–temperature variation fields whose dissipation energy has a temporal behavior lower than an appropriate growing exponential.