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

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 th...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-10, Vol.51 (10), p.103523-103523-17
Main Authors: Wehbe, Ali, Youssef, Wael
Format: Article
Language:English
Subjects:
Asymptotic methods
ASYMPTOTIC SOLUTIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COUPLING
DAMPING
DIFFERENTIAL EQUATIONS
EQUATIONS
Exact sciences and technology
FUNCTIONS
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
Mathematics
MOTION
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
Physics
POLYNOMIALS
ROTATION
Sciences and techniques of general use
STABILITY
Studies
VELOCITY
WAVE EQUATIONS
Waveform analysis
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3486094