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

Mohamed MELLAH; Ali HAKEM; Gongwei LIU

doi:10.4208/jpde.v37.n4.6

Journal of Partial Differential Equations ›› 2024, Vol. 37 ›› Issue (4) : 467 -481. DOI: 10.4208/jpde.v37.n4.6

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

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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.

Keywords

Viscoelastic equation / nonlinear boundary source / stabilization

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Mohamed MELLAH, Ali HAKEM, Gongwei LIU. Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term. Journal of Partial Differential Equations, 2024, 37(4): 467-481 DOI:10.4208/jpde.v37.n4.6