arXiv subjects

Mohamed Ferhat

Publications and source records attributed to Mohamed Ferhat.

3 recordsLinked to original sources

arXiv2022

Global existence and Asymptotic behavior for a system of wave equation in presence of distributed delay term

In this paper, we consider the following viscoelastic coupled wave equation with a delay term: $$ \begin{gathered} u_{tt}(x,t)-Lu(x,t)-\int_0^t g_1(t-σ)L u(x,σ)dσ+ μ_{1}u_{t}(x,t) + \int_{τ_1}^{τ_2} μ_2(s)u_{t}(x,t-s)ds + f_1(u,\upsilon)=0, \\ \upsilon_{tt}(x,t) - L\upsilon(x,t) - \int_0^t g_{2}(t-σ)L \upsilon(x,σ)dσ+ μ_3\upsilon_t(x,t) + \int_{τ_1}^{τ_2} μ_4(s)\upsilon_{t}(x,t-s)ds + f_{2}(u,\upsilon)=0, \end{gathered} $$ in a bounded domain. Under appropriate conditions on $μ_{1}$, $μ_{2}$, $μ_{3}$ and $μ_{4}$, we prove global existence result by combining the energy method with the Faedo-Galerkin's procedure. In addition , we focus on asymptotic behavior by using an appropriate Lyapunov functional.

math.AP↗

arXiv2018

A frequency approach for stabilization of one-dimensional degenerate wave equation

In this paper, we are concerned with the study of stabilization problem for the following strongly degenerate wave equation in one space dimension $$w_{tt}(x,t)-\left(x^αw_x(x,t)\right)_x=0$$ where ${\bfα\in [1,2)}$. Thus, using a frequency domain method inspired from \cite{BT}, we prove the polynomial decays of its total energy with $t^{-\nicefrac{1}{2}}$ decay rate.

math.AP↗

arXiv2018

Stability results for viscoelastic wave equation with dynamic boundary conditions

In this paper we consider wave viscoelastic equation with dynamic boundary condition in a bounded domain, we establish a general decay result of energy by exploiting the frequency domain method which consists in combining a contradiction argument and a special analysis for the resolvent of the operator of interest with assumptions on past history relaxation function.

math.AP↗