Stability and energy decay rates in linear thermoelasticity^∗

^∗Research performed under the auspices of G.N.F.M. - C.N.R. and partially supported by Italian M.U.R.S.T.

Abstract

We consider the initial-boundary value problem for a linear thermoelastic material characterized by Cattaneo-Maxwell's constitutive equation for the heat flux. We prove existence and uniqueness theorems for weak and strong solutions of the evolutive problem. Moreover, the dissipative effects of Cattaneo-Maxwell's relation allow us to prove, for the unidimensional model, the exponential decay of the energy associated to the system.

Keywords:

• Linear thermoelasticity
• dissipative system
• asymptotic behavior
• energy decay rates

^∗Research performed under the auspices of G.N.F.M. - C.N.R. and partially supported by Italian M.U.R.S.T.

^†Dipartimento di Matematica Applicata “U.Dinin ”, FacoltH di Ingegneria, via Diotisalvi 2, 56126-Pisa (Italy).

^‡Dipartimento di Matematica, Universit´ di Bologna, Piazza di Porta S.Donato 5, 40127-Bologna (Italy).

^∗Research performed under the auspices of G.N.F.M. - C.N.R. and partially supported by Italian M.U.R.S.T.

^†Dipartimento di Matematica Applicata “U.Dinin ”, FacoltH di Ingegneria, via Diotisalvi 2, 56126-Pisa (Italy).

^‡Dipartimento di Matematica, Universit´ di Bologna, Piazza di Porta S.Donato 5, 40127-Bologna (Italy).

Notes

^∗Research performed under the auspices of G.N.F.M. - C.N.R. and partially supported by Italian M.U.R.S.T.

^†Dipartimento di Matematica Applicata “U.Dinin ”, FacoltH di Ingegneria, via Diotisalvi 2, 56126-Pisa (Italy).

^‡Dipartimento di Matematica, Universit´ di Bologna, Piazza di Porta S.Donato 5, 40127-Bologna (Italy).