The contact problem in thermoviscoelastic materials

We stablish an existence result for the thermoviscoelastic degenerated contact problem. The nonlinear stress-strain relation we will consider here is given by where M is a function satisfying M ∈ C¹(]0, ∞[) ∩ C([0, ∞[), M(s) ≥ C s ^p. Moreover, we show that the solution decays uniformly to zero. That is, denoting by E(t) the first-order energy associated to the equation, we show that there exist positive constants C satisfying E(t) ≤ C(E(0))(1 + t)^{-(p + 2)/p} where p is a positive number which depends on nonlinear terms of the system.