Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations

In this paper, we study a class of semilinear pseudo-parabolic equations. By introducing a family of potential wells, we prove the invariance of some sets, global existence, nonexistence and asymptotic behavior of solutions with initial energy J(u0)⩽d. Moreover, we obtain finite time blow-up with high initial energy J(u0)>d by comparison principle.