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

Wenjun Liu, Hefeng Zhuang
2017 unpublished
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
more » ... of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.
doi:10.20944/preprints201702.0057.v2 fatcat:3elhmnvapzcr3bqcpxi7r5qvae