J. Korean Math. Soc. 2005; 42(6): 1137-1152
Printed November 1, 2005
Copyright © The Korean Mathematical Society.
Jong Yeoul Park and Joung Ae Kim
Pusan National University, Pusan National University
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
MSC numbers: 35B40, 35L75, 74K10, 39A11
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