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

In this paper, a nonlocal semilinear pseudo‐parabolic ‐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.