On Modeling and Uniform Stability of a Partially Dissipative Viscoelastic Timoshenko System

Effects of history and heat models on the stability of thermoelastic Timoshenko systems

“…with an exponentially decaying positive kernel g, also becoming exponentially stable if and only if the EWS condition (1.2) is satisfied, see [14,21]. A short survey of references containing more recent generalized results concerning the models (1.3) and (1.5) can be found in [3]. Combining history and thermal effects, in [14], the thermo-(visco-)elastic system 6) was considered and once more, for exponentially decaying kernels g, the exponential stability of the system was obtained if and only if the EWS condition (1.2) is satisfied.…”

“…where we have α = 0 (without history) or α = 1 (with history), and τ = 0 (Fourier law) or τ > 0 (Cattaneo law). For the derivation of these possible dissipative hybrid models generated by (1.10), we refer to [2,3] where physical justifications are provided on thermo-(visco-)elasticity. The remaining constants are assumed to be positive constants, 11) and further conditions on the exponentially decaying kernel g will be specified later on.…”

Decay rates for the energy of a singular nonlocal viscoelastic system

“…For more results in this direction, see previous studies. [38][39][40][41] However, previous studies1-32, [33][34][35][36][37][38][39][40][41][42][44][45][46] did not study the decay rates for the energy of system (1)- (3). Motivated by the above research, we will consider the intrinsic decay rates for the energy of relaxation kernels described by the inequality g ′ i (t) ≤ −H (g i (t)) , (i = 1, 2) for all t ≥ 0, of the model (1)-(3) in this paper.…”

“…Gomes et al 36 studied the decay rates for a class of nonlinear viscoelastic plate models. Alves 37 studied the modeling and uniform stability of a partially dissipative viscoelastic timoshenko system. For more results in this direction, see previous studies 38‐41 …”

“…However, previous studies1‐32, 33‐42,44‐46 did not study the decay rates for the energy of system ()–(). Motivated by the above research, we will consider the intrinsic decay rates for the energy of relaxation kernels described by the inequality for all t ≥ 0, of the model ()–() in this paper.…”