Exponential stability for a thermoelastic laminated beam with nonlinear weights and time-varying delay

Abstract

In this paper, we study the well-posedness and asymptotic stability to a thermoelastic laminated beam with nonlinear weights and time-varying delay. To the best of our knowledge, there are no results on the system and related Timoshenko systems with nonlinear weights. On suitable premises about the time delay and the hypothesis of equal-speed wave propagation, existence and uniqueness of solution is obtained by combining semigroup theory with Kato variable norm technique. The exponential stability is proved by energy method in two cases, with and without the structural damping, by using suitably sophisticated estimates for multipliers to construct an appropriated Lyapunov functional.

Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

“…Since then, a great interest has been aroused in different contexts and nowadays there are many results on global and local solutions, stability, and burst behavior of solutions in thermoelasticity theory. We can cite [2][3][4][5][6][7][8][9][10][11] with references therein.…”

Asymptotic behavior of a laminated beam with nonlinear delay and nonlinear structural damping

“…Using dissipation through structural and thermoelastic damping, the authors established exponential and polynomial decay results with some restriction of the parameters provided that β > τ 2 τ 1 |µ 2 (ϱ)|dϱ. Lastly, Nonato et al [37] recently studied a thermoelastic laminated beam with nonlinear weights and time-varying delay. With help of the dissipation through thermal effect and nonlinear frictional damping, the authors established exponential decay with and without the structural damping with suitable relationship between friction damping and delay weight, provided the condition of equal wave speeds holds.…”

Stabilization of swelling porous elastic soils with fluid saturation, time varying-delay and time-varying weights

“…There are also several studies considering nonlinear models with a delay where the existence of attractors is investigated, among them, Timoshenko systems [7,9,20,25], poroelastic systems [6] and suspension bridge [18,42]. Based on the work mentioned above about the problem of swelling of the one-dimensional porous elastic soils and in references [40,41], we design and propose to study the exponential stability for the following system…”