TY - JOUR
T1 - Global Existence and Stability for a Viscoelastic Wave Equation with Nonlinear Boundary Source Term
AU - Mellah , Mohamed
AU - Hakem , Ali
AU - Liu , Gongwei
JO - Journal of Partial Differential Equations
VL - 4
SP - 467
EP - 481
PY - 2024
DA - 2024/12
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n4.6
UR - https://global-sci.org/intro/article_detail/jpde/23691.html
KW - Viscoelastic equation, nonlinear boundary source, stabilization.
AB - <p style="text-align: justify;">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.</p>