GLOBAL EXISTENCE AND ASYMPTOTIC-BEHAVIOR IN NONLINEAR THERMOVISCOELASTICITY

We study global existence, uniqueness, and asymptotic behavior, as tim e tends to infinity, of weak solutions to the system of nonlinear ther moviscoelasticity. Various boundary conditions are considered. It is s hown that for any initial data (u(0), v(0), O-0) is an element of L(in finity) x W-I.infinity x H-1 there is a unique global solution (u, v, O)= (deformation gradient, velocity, temperature) such that u is an el ement of C([0, infinity], L(infinity)), v is an element of C((O, infin ity), W-1.infinity) boolean AND L(infinity)([O, infinity), 0 is an ele ment of C(0, infinity), H-1). The constitutive assumptions for the Hel mholtz free energy include the models for the study of phase transitio n problems in shape memory alloys. (C) 1997 Academic Press.