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GLOBAL EXISTENCE AND STABILITY FOR EULER-BERNOULLI BEAM EQUATION WITH MEMORY CONDITION AT THE BOUNDARY

  • Park, Jong-Yeoul (Department of Mathematics College of Science Pusan National University) ;
  • Kim, Joung-Ae (Department of Mathematics College of Science Pusan National University)
  • Published : 2005.11.01

Abstract

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

Keywords

global existence;Euler-Bernoulli beam equation;Galerkin method;boundary value problem

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