Journal Articles

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Open Access
Anisotropic non-local problems: asymptotic behaviour and existence results
(Université de M'sila, 2021) Ahlem Yahiaoui; Senoussi Guesmia; Abdelmouhcene Sengouga
We deal with anisotropic singular perturbation problems in some weighted spaces of Sobolev type. The perturbed problems are elliptic, semi-linear and non-local. Using a variational approach, we establish the existence of their solutions as critical points of some C1- functionals. Besides, we study the asymptotic behaviour of these solutions with respect to the parameter of perturbation ε and, as ε → 0, we obtain existence results for some non-standard integrodifferential problems. A non-local eigenvalue problem related to the considered problems is also investigated and used to carry out this study.
Open Access
Exponential stability estimates for an axially travelling string damped at one end
(université msila, 2023) Seyf Eddine Ghenimi; Abdelmouhcene Sengouga
We study the small vibrations of an axially travelling string with a dashpot damping at one end. The string is modelled by a wave equation in a timedependent interval with two endpoints moving at a constant speed v. For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower exponentially decaying estimates for the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case v = 0