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http://dx.doi.org/10.4134/JKMS.2005.42.6.1137

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)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.6, 2005 , pp. 1137-1152 More about this Journal
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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