Exponential stabilization of the Timoshenko system by a thermal effect with an oscillating kernel

Abstract

a b s t r a c tIn this paper, we consider a Timoshenko system supplemented by a heat equation with a viscoelastic damping term. We prove an exponential decay of solutions under weak assumptions. The kernels we consider here are weaker than the ones used usually in viscoelasticity. This kind of thermal damping was first introduced by Rivera and Racke (2002) [1] and then modified according to the Green and Naghdi theory Naghdi (1991, 1992) [2,3]) by the present authors, Djebabla and Tatar (2010) [4].

Energy decay result in a Timoshenko‐type system of thermoelasticity of type III with weak damping

“…In the presence of the thermo‐viscoelastic damping, Djebabla and Tatar considered the following Timoshenko system where ρ 1 , ρ 2 , ρ 3 , k , b , β , l , and γ are positive constants. They proved the exponential decay of solutions in the energy norm if and only if the coefficients satisfy and g decays uniformly.…”

Existence and general stabilization of the Timoshenko system with a thermo-viscoelastic damping and a delay term in the internal feedback

“…As in [6] and [3], we construct approximations of the solution (Φ, Ψ, θ, z) by the Faedo-Galerkin method as follows. For every n ≥ 1, let W n =span{ω 1 , .…”

New stability number of the Timo- shenko system with only microtemperature effects and without thermal conductivity1

“…In recent decades, research on Timoshenko type systems has been studied by fairly a large number of researchers, and an increasing interest has been developed to determine the asymptotic behavior by using several different dampings (frictional, structural, viscoelastic) linear, nonlinear, with and without coupling with a heat equation have been treated see ( [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] and [14]). Recently, an essential problem was addressed about the minimal dissipation required to get exponential decay.…”