General decay for a viscoelastic-type Timoshenko system with thermoelasticity of type III

General decay for memory-type porous elastic system with thermoelasticity of type III

“…The well-posedness of ( 1)-( 3) is given by the following proposition which can be established using Faedo-Galerkin method (see [9,10]).…”

“…For more results on thermoelasticity of type III and porous elasticity, we refer the reader to [8,9,[15][16][17][18][19]27] and the references therein.…”

Finite Element Error Analysis of a Viscoelastic Timoshenko Beam with Thermodiffusion Effects

“…In this way, in [2,3] the energy decay rates were analyzed when the past history was assumed; in [4], the socalled Kelvin-Voigt dissipation was considered; in [5], a new dynamic thermoviscoelastic contact problem was studied including a frictional contact; in [6], the uniform stability of a partially dissipative viscoelastic Timoshenko system was obtained; in [7], the energy decay was proved for a Timoshenko system with a memory type; the second sound effect was included in [8,9]. The nonexponential and polynomial energy decay was shown in [10,11] for a Kelvin-Voigt damping with heat conduction; the well-posedness and the energy decay (polynomial or exponential, depending on the speeds of wave propagation) was studied in [12] for a thermoelastic laminated Timoshenko beam; type III thermoelasticity was included in [13,14]; the long-time dynamics of a Timoshenko system modeling vibrations of beams with nonlinear localized damping mechanisms was derived in [15]; the global stability of Timoshenko systems was considered in [16]; and the well-posedness and regularity of the viscoelastic Timoshenko beam model, including a comparison with the widely used Euler-Bernoulli model, is provided in [17].…”