Global well-posedness for pseudo-parabolic p-Laplacian equation with singular potential and logarithmic nonlinearity

Abstract

The main goal of this work is to investigate the initial boundary value problem for a class of pseudo-parabolic p-Laplacian equations with singular potential and logarithmic nonlinearity. First of all, we prove the local existence of weak solutions. Second, we show the existence of the global solution and the weak solution converging to the stationary solution when the time tends to infinity, and we show blow-up phenomena of solutions with the initial energy less than the mountain pass level d by using the potential well method. Finally, we parallelly stretch all the conclusions for the subcritical case to the critical case.