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GLOBAL EXISTENCE AND STABILITY FOR EULER-BERNOULLI BEAM EQUATION WITH MEMORY CONDITION AT THE BOUNDARY
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 Title & Authors
GLOBAL EXISTENCE AND STABILITY FOR EULER-BERNOULLI BEAM EQUATION WITH MEMORY CONDITION AT THE BOUNDARY
Park, Jong-Yeoul; Kim, Joung-Ae;
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 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;
 Language
English
 Cited by
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Uniform Decay for Solutions of an Axially Moving Viscoelastic Beam, Applied Mathematics & Optimization, 2016  crossref(new windwow)
2.
Energy Decay for the Strongly Damped Nonlinear Beam Equation and Its Applications in Moving Boundary, Acta Applicandae Mathematicae, 2010, 109, 2, 507  crossref(new windwow)
3.
Stability of an Axially Moving Viscoelastic Beam, Journal of Dynamical and Control Systems, 2016  crossref(new windwow)
4.
Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type, Journal of Dynamical and Control Systems, 2016  crossref(new windwow)
5.
On the exponential decay of the Euler–Bernoulli beam with boundary energy dissipation, Journal of Mathematical Analysis and Applications, 2012, 389, 2, 1078  crossref(new windwow)
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