On a One-Dimensional Nonlinear Thermoviscoelastic Model for Structural Phase Transitions in Shape Memory Alloys

We shall prove the existence and the uniqueness of global classical solutions of the following one-dimensional Landau-Devonshire thermoviscoelastic model for structural phase transitions in shape memory alloys: utt−p(θ, ux)x−μuxxt = ƒ, in (0, 1)×(0, T)α1 θt−κθxx−α2θ uxuxt−μu2xt = g, in (0, 1)×(0, T)u(0, t) = u(1, t) = 0, θx(0, t) = θx(1, t) = 0u(x, 0) = u0(x), ut(x, 0) = u1(x), θ(x, 0) = θ0(x).