Stability of a thermoelastic laminated system subject to a neutral delay

Abstract

In this work, we consider a system of two identical beams of uniform thickness modeled as a Timoshenko system. The slip between the beams is taken into account, and the system is coupled with a heat equation. Moreover, the slip equation is subject to a distributed delay of neutral type. Delays are known to be of a destructive nature in general. Therefore, here, the delay will compete with a frictional damping and the dissipation produced by the heat equation. We provide sufficient conditions ensuring exponential and polynomial stability of the structure. KEYWORDSexponential decay, laminated beams, multiplier technique, neutral delay, stability, timoshenko system MSC CLASSIFICATION 35L20; 93D15; 93D20where h is a nonnegative nonincreasing differentiable function. This problem models, for instance, acoustic wave propagation. Reasonable conditions on the distributed neutral delay ensuring exponential stability have been established there.

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“…In [25] Seghour et al studied the following thermoelastic laminated system with neutral delay 8 > > > > < > > > > : with boundary conditions…”

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“…With help of three boundary controls to create necessary damping, the author proved wellposedness and exponential decay of the solution provided 4GL 2 π 2 ⩽ D and, delay weights satisfying 0 ⩽ a i < a 0 i , i = 1, 2, 3 where a 0 i depends on the parameters of the system. Seghour et al [41] investigated a thermoelastic laminated beam with neutral delay in dynamics of slip equation. In addition to the dissipation through thermal effect, the authors introduced a linear frictional damping term in the transverse displacement to establish exponential stability for ρ = GI ρ and, polynomial decay otherwise.…”