Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2005; 42(6): 1137-1152

Printed November 1, 2005

Copyright © The Korean Mathematical Society.

Global existence and stability for Euler-Bernoulli beam equation with memory condition at the boundary

Jong Yeoul Park and Joung Ae Kim

Pusan National University, Pusan National University

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

MSC numbers: 35B40, 35L75, 74K10, 39A11