IDENTIFYING MEMORY KERNELS IN LINEAR THERMOVISCOELASTICITY OF BOLTZMANN TYPE
Cecilia Cavaterra, Maurizio Grasselli · Mathematical Models and Methods in Applied Sciences · 1994
The evolution of the displacement u and the temperature ϑ in a three-dimensional, linear, thermoviscoelastic material of Boltzmann type is governed by a system of two coupled Volterra integrodifferential equations. The damping mechanism is characterized by some time-dependent memory kernels which are a priori unknown. These kernels are identified via measurements of boundary tractions and localized temperatures, provided that the pair (u, ϑ) solves a suitable initial and boundary value problem for the evolution system.