Some New Results on the Global Existence and Blow-Up for a Class of Pseudo-parabolic Equation

This paper is devoted to the study of the global existence and blow-up for a class of pseudo-parabolic equation. We first obtain two new proofs for the blow-up results which only depends on Nehari functional but not on energy levels, the present methods may be more applicable to relevant systems. Then, we give the exact blow-up rate and a new upper bound of the blow-up time for the problem, which improves a recent existing conclusion. Finally, we built a new global boundedness result under an explicit small data which is also independent of initial energy. Through these research, we propose a new insight about the condition which generates the global bounded solution or finite time blow-up solution.