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

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

Year:    2024

Author:    Mohamed Mellah, Ali Hakem, Gongwei Liu

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 467–481

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 467–481

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Viscoelastic equation nonlinear boundary source stabilization.

Author Details

Mohamed Mellah

Ali Hakem

Gongwei Liu