Existence and decay rates for a coupled Balakrishnan‐Taylor viscoelastic system with dynamic boundary conditions

Abstract

In this paper, we are concerned with a coupled viscoelastic wave system with Balakrishnan‐Taylor dampings, dynamic boundary conditions, source terms, and past histories. Under suitable assumptions on relaxation functions and source terms, we prove the global existence of solutions by potential well theory and we establish a more general decay result of energy, in which the exponential decay and polynomial decay are only special cases, by introducing suitable energy and perturbed Lyapunov functionals.

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].…”

Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

“…In [2], Balakrishnan and Taylor proposed a new model of damping called the Balakrishnan-Taylor damping, as it relates to the span problem and the plate equation. For more depth, here are some papers that focused on the study of this damping: [2,3,8,10,16,18,20,27,35].…”

Growth and blow-up of solutions with positive initial energy for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, delay and Balakrishnan-Taylor damping terms

“…Here, the memory term's kernel function is denoted by ℶ. See ( [8], [13], [15], [20], [21], [22], [29]).…”

“…In [3], Taylor and Balakrishnan introduced a novel damping model termed the Balakrishnan-Taylor damping, which pertains to the span problem and the plate equation. For further exploration, several papers have delved into the study of this damping phenomenon ( [3], [6], [11], [15], [21], [22], [28], [31]).…”