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This paper is concerned with global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions. The constitutive assumptions for the Helmholtz free energy include the model for the study of phase transitions in shape memory alloys. To describe phase transitions between different configurations of crystal lattices, we work in a framework in which the strain u belongs to L°°. It is shown that for any initial data of (strain, velocity, absolute temperature) (uo,vo>#o) G L°° x Wq'°° xH1, there is a unique global solution (it, v,6) £ C([0, +oo]; L°°) xC(0, +oo); JTo1'00) fl L°°([0, +oo); W1'00) x C([0, +oo); H1). Results concerning the asymptotic behavior as time goes to infinity are obtained. A new approach is introduced and more delicate estimates are derived to obtain the crucial L°°-norm estimate of u.

Global existence and asymptotic behavior of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions