EXISTENCE AND CONVERGENCE RESULTS FOR A NONLINEAR THERMOELASTIC CONTACT PROBLEM

In this paper, we consider a thermoelastic contact problem in which the heat exchange boundary condition is affected by normal displacement on contact boundary, and the operator in the nonlinear thermoelastic constitutive law is considered to rely on temperature field. First, we deliver the weak formulation of the thermoelastic contact problem which is a coupled system formulated by two variational inequalities with constraints. Then, by employing the Tychonoff fixed point theorem for multivalued operators, an existence theorem for the thermoelastic contact problem is established. Finally, a family of approximate penalized problems corresponding to the thermoelastic contact problem is introduced, and a convergence result is proved. The latter indicates that the solution set of the thermoelastic contact problem can be approached by the solution sets of approximate penalized problems in the sense of the upper semicontinuity property of Kuratowski.