Analysis of a thermo-viscoelastic antiplane contact problem with long-term memory

We study a mechanical problem modeling the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The material is assumed to be thermo-viscoelastic with long-term memory, the process is quasistatic, and the friction is modeled with Tresca’s law. The mechanical model is described as a coupled system of a variational elliptic equality for the displacements and a differential heat equation for the temperature. We present a variational formulation of the problem and establish the existence and uniqueness of weak solution in using general results on evolution equations with monotone operators and fixed point arguments.