On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

Abstract

<abstract><p>This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms.</p></abstract>

General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions

“…Suppose that (H1)-(H5) hold. Then, for any T > 0, there exists a unique pair of functions (u, w, v) that are the solution to problems ( 22)- (28) in the class…”

“…Assume that (H1) and (H2) hold and that G is nonlinear. Then, the solution to ( 22)- (28) satisfies the estimates…”

“…As far as we know, there are few results for the viscoelastic wave equation with a nonlinear time-varying delay. Recently, Djeradi et al [28] and Mukiawa et al [29] showed the stability of the thermoelastic laminated beam and thermoelastic Timoshenko beam with nonlinear time-varying delay, respectively. The papers introduced so far have studied the energy decay rate of the solution for the equation with nonlinear time-varying delay in the Dirichlet boundary condition.…”