Existence and New General Decay Results for a Viscoelastic Timoshenko System

Abstract

In this paper, we are concerned with a memory-type Timoshenko system with Dirichlet boundary conditions and a very general class of relaxation functions. We prove the existence and uniqueness of solutions of the system as well as some new decay results which generalize and improve many earlier ones in the literature. We consider the case of equal-speeds and the case of non-equal-speeds of propagation. We also give some numerical illustrations and related comparisons.

Asymptotic stability of porous-elastic system with thermoelasticity of type III

“…For more stability, we implement the conservative scheme of Lax-Wendroff. for more details, we refer to our previous works [1,11,17]. We examine the following two tests:…”

Optimal Decay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate

“…For the following values of the parameter σ � 0.1, 1, 5, we simulate six tests of the decay of the energy (19) (for similar constructions, we refer to [41,42]). Test 1: in the first three tests, we present the decay case using the exponential function g 1 (t) = e − 2t , the vector field (103), and the parameters σ = 0.1, 1, 5 (Test 1.1, 1.2, and 1.3).…”

Adaptive stabilization of a Timoshenko system by boundary feedback controls

“…Timoshenko system received considerable attention from various researchers and many questions related to well-posedness and long-time behavior of the equation with internal feedback controls had been investigated, see the literature. [1][2][3][4][5][6] For Timoshenko systems with boundary feedback controls, we start by reporting the work of Kim and Renardy 7 in which the authors studied a Timoshenko system with clamped boundary conditions at the left end and linear boundary controls at the right end. By using the multiplier method, they proved the exponential stability of the system.…”

“…The main purpose of this work is to analyze the global existence and asymptotic stability of the undamped Timoshenko system (1). We study System (1) under the influence of the following high gain adaptive boundary controls:…”

“…Therefore, the Timoshenko model describes the dynamics behavior of the beam more accurately than the Euler‐Bernoulli beam model in this situation. Timoshenko system received considerable attention from various researchers and many questions related to well‐posedness and long‐time behavior of the equation with internal feedback controls had been investigated, see the literature 1–6 …”