Abstract
In this paper, a semilinear fourth-order Petrovsky equation with nonlinear weak damping term and linear strong damping term is considered in the frame of the potential well. We prove the existence and uniqueness of the global strong solution with sub-critical initial energy. In addition, we obtain the global existence, asymptotic behaviour and finite time blowup for the weak (non-steady state) solution with a critical initial energy level.
Disclosure statement
No potential conflict of interest was reported by the author(s).