Zayd Hajjej

In this paper, we study a semilinear Timoshenko beam system posed in one dimensional inhomogeneous medium. This study focuses on the stability analysis of such a problem under the effect of two localized delayed damping mechanisms. Despite the presence of a time delay, we are able to prove that the system is well-posed in the sense of semigroups theory. Unlike previous works, we show that the exponential decay of the energy of our system can be ensured by a locally distributed delayed damping alone. This result is established under the usual conditions on the damping parameters, namely that the weights of the time delays are smaller than those of the corresponding dampings, regardless of the wave propagation speeds. The proof of our main stability result relies on some techniques from the microlocal analysis theory.

This paper is concerned with the long-time dynamics of the model of a laminated Timoshenko beam, which is a structure given by two-layered beams with structural damping as a result of an interfacial slip, with nonlinear localized damping mechanisms placed on an arbitrarily small support. We prove that the system admits a global attractor which is characterized as an unstable manifold of the set of stationary solutions. The regularity and finite fractal dimension of the global attractor is also proved. Finally, we obtain the existence of a generalized exponential attractor. All results are proved without any restrictions on the coefficients and the assumption of equal wave speed propagation.

This paper addresses a Lamé system with a nonlinear logarithmic source term, incorporating an infinite memory term and fractional damping. We first prove the well-posedness of the problem by using the semigroup method. Then, we investigate its exponential stability by constructing a suitable Lyapunov functional.

This study examines a nonlinear wave equation with boundary fractional damping and time-varying delay. After proving the existence of a global solution, we establish exponential stability by constructing an appropriate Lyapunov functional. Finally, we prove the blow-up phenomenon using the potential-well method.

In this study, we examine a q-Kirchhoff-type equation defined on a bounded domain, incorporating nonlinear boundary damping and source terms with variable exponents. Assuming appropriate conditions on the initial data and the variable exponent functions, we establish the global existence of solutions. Subsequently, we derive a general decay estimate for these solutions. Lastly, we demonstrate that solutions with negative initial energy exhibit finite-time blow-up.

This paper studies a one-dimensional thermoelastic Bresse beam model, in which thermal effects governed by the Green–Naghdi theory of heat conduction are coupled specifically with the longitudinal displacement. Assuming appropriate conditions on the memory kernel and by defining a key stability parameter, we prove a unified decay estimate for the system’s energy. This general result includes both exponential and polynomial decay rates as special instances, offering a comprehensive framework for characterizing the system’s long-term behavior.

In this work, we study a nonlinear system of p-Biharmonic hyperbolic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the initial data and the damping terms, we establish the global existence of solutions. Furthermore, we derive a general decay result, and finally, we prove the occurrence of blow-up for solutions with negative initial energy.

We correct a mistake in the proof of Proposition 2.2 and add explanatory sentences in the proof of Theorem 3.2 of our paper.