UNIFORM DECAY OF A VISCOELASTIC NONLINEAR BEAM IN TWO DIMENSIONAL SPACE
BILLAL LEKDIM
Faculty of Mathematics, University of Sciences and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria.
AMMAR KHEMMOUDJ *
Faculty of Mathematics, University of Sciences and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper we study a viscoelastic nonlinear beam in two-dimensional space. We establish the well-posedness and a decay result. The proposed boundary controller guarantees that when there are no external forces, the beam is globally exponentially stabilized at its equilibrium position and that when the forces are presented, the beam is stabilized at the neighborhood of its equilibrium position. The method is based on the multiplier technique and some ideas introduced in [1].
Keywords: Uniform decay, viscoelastic, nonlinear, memory terms, two-dimentionel space