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 M HL u 2 dx u u , x x x t ž / 0 where M is a function satisfying M C1Ž 0, . CŽ 0, ., MŽs. C s p. Moreover, we show that the solution decays uniformly to zero. That is, denoting by EŽt. the first-order energy associated to the equation, we show that there exist positive constants C satisfying EŽt. CŽEŽ0..Ž1 t. Žp 2. p where p is a positive number which depends on nonlinear terms of the system