Memory-type boundary control of a laminated Timoshenko beam

Abstract

<jats:p> In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel functions, we establish an optimal explicit energy decay result. The stability result is more general than previous works and hence improves earlier results in the literature. </jats:p>

Laminated Timoshenko beams with interfacial slip and infinite memories

“…Namely, under some restrictions on the parameters and with one or two kernels converging exponentially to zero at infinity, the exponential stability was proved in Lo and Tatar 1,8,22 . Similar stability results with finite or infinite memory terms were obtained in previous studies 23–27 …”

“…1,8,22 Similar stability results with finite or infinite memory terms were obtained in previous studies. [23][24][25][26][27] For the stability of Bresse systems 28 with infinite memories, we refer the readers to Guesmia 29,30 and Guesmia and Kirane, 31,32 and the references therein.…”

Memory‐type boundary stabilization of a transmission problem for Kirchhoff wave equations

“…Wu 11 used this assumption to study a Kirchhoff-type wave equation. Please see previous studies, [12][13][14][15][16][17][18][19] etc., for the results on wave equations with boundary condition of memory type.…”

A New General Decay Rate of Wave Equation with Memory-Type Boundary Control

“…Wu [22] used this assumption to study a wave Kirchhoff-type wave equation with a boundary control of memory type. For nonlinear wave equations with memorytype boundary condition, we refer to Cavalcanti and Guesmia [23], Feng [24], Feng et al [25][26][27], Muñoz Rivera and Andrade [28], and Zhang [29].…”