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The Long-Time Behavior of the Solution for the Two Classes of Dynamical Systems

Author: ZhouFuMin
Tutor: MaQiaoZhen
School: Northwest Normal University
Course: Applied Mathematics
Keywords: Suspension bridge equations Global attractor Semigroup Plate equation
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 2
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Abstract


Based on the theory of dynamical system, we consider the long-time be-haviors of the solution for the suspension bridge equation and Plate equation.In Chapter1, some preliminary results and important conclusions that we will used in this thesis are presented.In Chapter2, we study the following suspension bridge equation where β∈R. By applying the method of decomposing operator and con-structing compact operator in weighted space, the existence of global at-tractor is obtained in R1. Comparing with the similar problem in bounded domain, system is more difficult in verifying the necessary compactness of the semigroup.In Chapter3, we consider the following Plate equation where β∈R, Ω(?)Rn is a smooth bounded domain. Based on a new a priori estimate method, so-called asymptotic a priori estimate, the existence of a global attractor is proved for the Plate equation in a bounded domain.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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