Preprint Article Version 2 This version not peer reviewed

Global Existence, Asymptotic Behavior and Blow-up of Solutions for a Suspension Bridge Equation with Nonlinear Damping and Source Terms

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)

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

Journal reference: Nonlinear Differential Equations and Applications NoDEA 2017, 24
DOI: 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.

Subject Areas

suspension bridges; fourth order wave equation; nonlinear damping; source term; existence; blow up

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