A contact problem in generalized thermoelasticity

In this work we study a one-dimensional contact problem in generalized thermoelasticity under the Green-Lindsay theory. Unilateral contact with an elastic obstacle is assumed. We consider the quasi-static and the fully dynamic situations. We prove existence and uniqueness results and propose finite element approximations in space with backward Euler discretization in time. Stability results are given and some numerical experiments reported. The second sound effect of heat conduction is observed in the simulations.