Global existence and finite time blowup for a fractional pseudo-parabolic p-Laplacian equation

In this paper, we study the initial-boundary value problem for a fractional pseudo parabolic p-Laplacian type equation. First, by means of the imbedding theorems, the theory of potential wells and the Galerkin method, we prove the existence and uniqueness of global solutions with subcritical initial energy, critical initial energy and supercritical initial energy, respectively. Next, we establish the decay estimate of global solutions with subcritical initial energy, critical initial energy and supercritical initial energy, respectively. For supercritical initial energy, we also need to analyze the properties of ?-limits of solutions. Finally, we discuss the finite time blowup of solutions with subcritical initial energy and critical initial energy, respectively.