Wael Sleiman Youssef

Associate professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: Théorie du Côntrole des EDP

- present : Associate professor

Lebanese University - Faculty of Sciences 1
Hadath - Lebanon

Teaching 5 Taught Courses
(2014-2015) Math 102 - Real Analysis (Functions)

BS Mathematics

(2014-2015) Math 103 - Linear Algebra II (Vector Space)

BS Mathematics

(2014-2015) Math 105 - Integral Calculus

BS Mathematics

(2014-2015) Math 417 - Spectral theory

M1 Mathematics

(2014-2015) Math 303 - Lagrangian Mechanics

BS Mathematics

Conferences 10 participations
Publications 5 publications

In this paper, we study the exact controllability of a system of weakly coupled wave equations with an internal locally control acted on only one equation. Using a piecewise multiplier method, we show that, for a sufficiently large time T , the observation of the velocity of the firstcomponent ofthe solution on aneighborhood ofapart of the boundary allows us to get back a weakened energy of initial data of the second component of the solution, this if the coupling parameter is sufficiently small, but non vanishing. This result leads, by the HUM method, to prove that the total system is exactly controllable by means of one locally distributed control.

Exponential and polynomial stability of an elastic Bresse system with two locally distributed feedbacks 2010

In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.

Observabilit ́ e et controlabilit ́ e exacte indirecte interne par un controle localement distribu ́ e de systemes d’equations couplees 2010

Stabilization of the uniform Timoshenko beam by one locally distributed feedback 2010

In this article, we study the energy decay rate for an elastic Timoshenko system. This system consists of two coupled wave equations. Only the equation about the rotation angle is damped by one locally distributed feedback at the neighbourhood of the boundary. The equation for the transverse displacement of the beam is only indirectly damped through the coupling. First, we establish an exponential energy decay rate in the case of the same speed of propagation. Next, when the wave speeds are different, a polynomial-type decay rate is obtained. These results are proved by verifying the frequency domain conditions

Direct and Indirect observability and Exacte Controllability of the Bresse System


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