General energy decay in a Timoshenko-type system of thermoelasticity of type III with a viscoelastic damping

Abstract

In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type, where the heat conduction is given by Green and Naghdi theories. We prove a general decay result, from which the exponential and polynomial decays are only special cases.

Bresse system with infinite memories

“…Moreover, the case of nonequal speeds was studied, and a polynomial decay result was proved for solutions with smooth initial data. A more general decay result, from which the exponential and polynomial rates of decay are only special cases, was also established by Kafini . In this paper, the viscoelastic damping of the form is acting in the third equation only.…”

Modelamiento numérico y computacional de la viga de Timoshenko sujeto a cargas puntuales

“…donde, M (L, t) = b (L) ψ x (L, t) es el momento de flexión y I m es el momento de inercia de la extremidad. Para ver otros casos de sistema de Timoshenko con disipación, ver [5,7,8].…”

Boundary stabilization of a Bresse‐type system

“…For similar problems dealing with the stability theory of the Timoshenko systems with memory dissipation, the reader is referred to [11][12][13][14][15][16][17][18][19][20]. For other types of dissipations, see [21][22][23][24][25][26][27] The subject of stability of Bresse-type systems (or circular arch problem ) has received much attention in the last years. It is important to mention that in [28], Alabau-Boussouira et al studied the Bresse system with frictional dissipation working only on the angle displacement.…”

“…For similar problems dealing with the stability theory of the Timoshenko systems with memory dissipation, the reader is referred to . For other types of dissipations, see .…”