Parameter Continuity of the Solutions of a Mathematical Model of Thermoviscoelasticity

In this paper the continuity of the solutions of a mathematical model of thermoviscoelasticity with respect to the model parameters is proved. This was an open problem conjectured iIi [27J and [28]. The nonlinear partial differential equations under consideration arise from the conservation laws of linear momentum and energy and describe structural phase transitions in solids with non-convex Landau-Ginzburg free energy potentials. The theories of analytic semigroups and real interpolation spaces for maximal accretive operators are 'used to show that the solutions of the model depend continuously on the admissible parameters, in particular, on those defining the free energy. More precisely, it is shown that if {qn}~=l is a sequence of admissible parameters converging to q, then the corresponding solutions z(tj qn) converge to z(tj q) in the norm of the graph of a fractional power of the operator associated to the linear part of the system.