Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term | Journal of Partial Differential Equations

Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term

Authors

Mohamed Mellah
Ali Hakem
Gongwei Liu

DOI:

https://doi.org/10.4208/jpde.v37.n4.6

Keywords:

Viscoelastic equation, nonlinear boundary source, stabilization.

Abstract

This work considers the initial boundary value problem for a viscoelastic wave equation with a nonlinear boundary source term. Under suitable assumptions, we prove the existence of global weak solutions using the Galerkin approximation. Then, we give a decay rate estimate of the energy by making use of the perturbed energy method.

Downloads

Published

2024-12-16

Issue

Vol. 37 No. 4 (2024)

Section

Articles

Most read articles by the same author(s)

Gongwei Liu, Yangyang Lu, Hongwei Zhang, Energy Decay for a Type of Plate Equation with Degenerate Energy Damping and Source Term , Journal of Partial Differential Equations: Vol. 36 No. 3 (2023)
Gongwei Liu, Shuying Tian, Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem , Journal of Partial Differential Equations: Vol. 31 No. 3 (2018)
Fatima. Z. Mahdi, Ali Hakem, Global Existence and Asymptotic Stability for the Initial Boundary Value Problem of the Linear Bresse System with a Time-Varying Delay Term , Journal of Partial Differential Equations: Vol. 32 No. 2 (2019)
Hongwei Zhang, Gongwei Liu, Qingying Hu, Exponential Decay of Energy for a Logarithmic Wave Equation , Journal of Partial Differential Equations: Vol. 28 No. 3 (2015)
Mohamed Berbiche, Ali Hakem, Non-existence of Global Solutions for a Fractional Wave-diffusion Equations , Journal of Partial Differential Equations: Vol. 25 No. 1 (2012)
Mohamed Ferhat, Ali Hakem, Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term , Journal of Partial Differential Equations: Vol. 27 No. 4 (2014)