Blow-up for a nonlocal semilinear pseudo-parabolic p-Laplacian type equation

Abstract

In this paper, a nonlocal semilinear pseudo-parabolic $p$-Laplacian type equation is considered, and finite time blow-up of solution with different initial energy is proved. More precisely, the upper bound for the blow-up time of solution with subcritical initial energy is established by potential well method and concavity argument. When the initial energy is supercritical, we prove the finite time blow-up of solution and obtain the upper bound for the blow-up time by different invariant set and concavity inequality. Moreover, by constructing a new control functional and providing careful estimates, the lower bound for the blow-up time of solution is given.