Browsing by Author "Sabbagh, Zineb"

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    On the ν-th-order solutions for nonlinear viscoelastic wave equation with averaged damping in RN
    (Canadian University of Dubai, 2025) Guidad, Derradji; Sabbagh, Zineb; Bouhali, Keltoum
    This paper investigates the existence, uniqueness, and qualitative properties of ν-th-order solutions for a class of nonlinear viscoelastic wave equations with averaged damping in the whole space R n, n ≥ 3ν, ν ≥ 1. The model incorporates both linear memory effects and a time-averaged damping term, which captures a more realistic dissipation mechanism in complex media. By employing energy methods, stable set method, and an appropriate integral inequality, we establish the global well-posedness of higher-order solutions under suitable assumptions on the nonlinearity and initial data with minimal a priori mathematical restrictions on the parameters ν, q, p. The analysis extends previous results on lower-order formulations, providing a broader framework for understanding the dynamic response of viscoelastic materials with memory and damping
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    Well-posedness and stability for a viscoelastic Petrovsky equation with a localized nonlinear damping
    (Springer, 2023) Sabbagh, Zineb; Khemmoudj, Ammar; Abdelli, Mama
    In this paper, we consider a viscoelastic Petrovsky equation with localised nonlinear damping in bounded domain. The nonlinear damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo–Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, exponential decay results of the energy are established via suitable Lyapunov functionals