arXiv subjects

Mama Abdelli

Publications and source records attributed to Mama Abdelli.

6 recordsLinked to original sources

arXiv2021

Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term

In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + Δ^{2} u -μ_1g_1( Δ( u_t(x,t))) -μ_2g_2( Δ(u_t(x,t-τ))) =0. \end{align*} We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.

math.AP↗

arXiv2020

Well-posedness and exponential decay for the Euler-Bernoulli beam conveying fluid equation with non-constant velocity and dynamical boundary conditions

In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. We prove the existence and uniqueness of global solution under suitable assumptions on the tension of beam and on the parameters of the problem. Afterwards, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.

math.AP↗

arXiv2018

The universal bound property for a class of second order ODEs

We consider the scalar second order ODE u + |u | $α$ u + |u| $β$ u = 0, where $α$, $β$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 < $α$ < $β$ and moreover there is a constant C independent of the initial data such that $\forall$t > 0, u (t) 2 + |u(t)| $β$+2 $\le$ C max{t -- 2 $α$ , t -- ($α$+1)($β$+2) $β$--$α$ }.

math.DS↗

arXiv2016

Existence, uniqueness and global behavior of the solutions to some nonlinear vector equations in a finite dimensional Hilbert space

The initial value problem and global properties of solutions are studied for the vector equation: $\Big(\|u'\|^{l}u'\Big)'+\|A^{\frac{1}{2}}u\|^βAu+g(u')=0$ in a finite dimensional Hilbert space under suitable assumptions on $g$.

math.CA↗

arXiv2014

Pointwise controllability as limit of internal controllability for the beam equation

This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.

math.OC↗

arXiv2013

Global behavior of the Solutions to a Class of Nonlinear, Singular Second Order ODE

In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: $ (|u'|^{l}u')' + c|u'|^αu' + d|u|^βu=0$, where $α,β,l,c, d$ are positive constants. In particular, existence, uniqueness and regularity as well as optimal decay rates of solutions to 0 are obtained depending on the various parameters, and the oscillatory or non-oscillatory behavior is elucidated.

math.CA↗