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Generalized Elastic Beam Equation with Damping long time behavior

Author: ChenGuiWei
Tutor: YangZhiJian
School: Zhengzhou University
Course: Basic mathematics
Keywords: Beam equation Initial Boundary Long time behavior Global Attractor
CLC: TB123
Type: Master's thesis
Year: 2008
Downloads: 7
Quote: 0
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Abstract


This paper studies a class of weakly damped fourth order nonlinear wave equation with initial boundary value problem for a long time behavior . This equation is one-dimensional mathematical model of the beam vibration equation when λ = g = f = 0 , it describes both ends fixed distance apart as an elastic beam transverse motion ( see Woinowsky-Krigcr [5]). We will use the operator theory is transformed into an abstract Cauchy problem for equation where A = △ 2 , D (A) = H 4 ∩ H 0 2 . then we give a priori estimates and proof of understanding with the Galerkin method , respectively, in the space C (R ; D (A 1/2 )) ∩ C 1 (R ; H) and C (R ; D (A 3/4 ) ) ∩ C (R ; D (A 1/4 )) the existence and uniqueness and continuous dependence on initial solution , which we define C < sub> 0 - semigroup where X = D (A 1/2 ) × H, X 1 = D (A 3/4 < / sup>) × D (A 1/4 ). tight asymptotic methods we use proven C 0 - semigroup S (t) , respectively, in the phase space X and X 1 in the existence of global attractors . Finally , we give an example to illustrate the theories on specific issues related to the application .

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CLC: > Industrial Technology > General industrial technology > Engineering and basic science > Engineering Mechanics > Engineering Vibration
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