Parameter Continuity of the Solutions of a Mathematical Model of Thermoviscoelasticity

PEDRO MORIN AND RUBEN D. SPIES

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

Unión Matemática Argentina

Lugar: Bahía Blanca; Año: 1996 vol. 40 p. 111 - 126

0041-6932

In this paper the continuity of the solutions of a mathematical model of thermoviscoelasticity with respect to the model parameters is proved. this wasan open problem conjectured in [27] 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} is a sequence of admissible parameters converging to q, then the corresponding solutions z(t;qn) converge to z(t;q) in the norm of the graph of a fractional power of the operator associated to the linear part of the system.