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Global Existence, Asymptotic Behavior and Blow-up of Solutions for a Suspension Bridge Equation with Nonlinear Damping and Source Terms
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Version 1
: Received: 16 February 2017 / Approved: 16 February 2017 / Online: 16 February 2017 (08:40:48 CET)
Version 2 : Received: 24 February 2017 / Approved: 24 February 2017 / Online: 24 February 2017 (09:06:57 CET)
Version 2 : Received: 24 February 2017 / Approved: 24 February 2017 / Online: 24 February 2017 (09:06:57 CET)
A peer-reviewed article of this Preprint also exists.
Liu, W. & Zhuang, H. Nonlinear Differ. Equ. Appl. (2017) 24: 67. https://doi.org/10.1007/s00030-017-0491-5 Liu, W. & Zhuang, H. Nonlinear Differ. Equ. Appl. (2017) 24: 67. https://doi.org/10.1007/s00030-017-0491-5
Abstract
In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |ut|m-2ut and source term |u|p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time Tmax is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.
Keywords
suspension bridges; fourth order wave equation; nonlinear damping; source term; existence; blow up
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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