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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 05 > No. 1

 
   

A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping

PP: 17-28
Author(s)
C. A Raposo, W. D. Bastos, J. A. J. Avila,
Abstract
In this work we consider a transmission problem for the longitudinal displacement of a Euler-Bernoulli beam, where one small part of the beam is made of a viscoelastic material with Kelvin-Voigt constitutive relation. We use semigroup theory to prove existence and uniqueness of solutions. We apply a general results due to L. Gearhart [5] and J. Pruss [10] in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is exponentially stable. A numerical scheme is presented.

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