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Corpus ID: 235458658

On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph

@inproceedings{Mahinzaeim2021OnTS,
title={On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph},
author={Mahyar Mahinzaeim and Gen Qi Xu and Hai Zhang},
year={2021}
}

. We deal with the as yet unresolved exponential stability problem for a stretched Euler–Bernoulli beam on a star-shaped metric graph with three identical edges. The edges are hinged with respect to the outer vertices. The inner vertex is capable of both translation and rotation, the latter of which is subject to a combination of elastic and frictional eﬀects. We present detailed results on the asymptotic distribution and structure of the spectrum of the linear operator associated with the… Expand

. We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of ﬁnite length conveying an ideal ﬂuid. The boundary conditions considered… Expand

This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more… Expand

THEOREM I. Assume that the operator F generates in the Hilbert space X the C0-semigroup etF, and assume that o(F) is discrete and can be partitioned into the subsets { n}n=l to each of whicN… Expand

The eigenvalue problem y(4)(λ, x) − (gy′)′(λ, x) = λ2y(λ, x) with boundary conditions y(λ, 0) = 0, y′′(λ, 0) = 0, y(λ, a) = 0, y′′(λ, a) + iαλy′(λ, a) = 0 is considered, where g ∈ C1[0, a] and α > 0.… Expand

A systematic survey of the theory of linear evolution equations in Banach spaces, reviewed in the period 1968–1982 in Ref. Zh. Matematika, is presented.