Mathematical analysis of a viscoelastic problem with temperature-dependent coefficients - Part I: Existence and uniqueness

The aim of this article is to study the quasistatic evolution of a thermoviscoelastic problem whose behaviour law is of the MaxwellNorton type with coefficients depending on temperature. In this law, the deformation rate tensor is a superposition of viscoelastic and thermal contributions. The existence and uniqueness of the solution is proved.