Affiliations: Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via E. Bonardi 9, 20133 Milano, Italy. E-mail: maurizio.grasselli@polimi.it | Laboratorio Nacional de Computaçao Cientifica, Av. Getúlio Vargas 333, 25651-070-Petropolis, Brazil. E-mail: rivera@lncc.br | Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy. E-mail: marco.squassina@univr.it
Note: [] Author was partially supported by the Italian PRIN Research Project 2006 Problemi a frontiera libera, transizioni di fase e modelli di isteresi.
Note: [] Author was partially supported by the Italian PRIN Research Project 2007 Metodi variazionali e topologici nello studio di fenomeni non lineari.
Abstract: We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial differential equation ruling the evolution of the vertical deflection, presenting a convolution term accounting for memory effects. It is also assumed that the thermal power contains a memory term characterized by a relaxation kernel. We prove that the system is exponentially stable and we obtain a closeness estimate between the system with memory effects and the corresponding memory-free limiting system, as the kernels fade in a suitable sense.
