A new blow-up criterion for a $p$-Laplacian type pseudo-parabolic equation with singular potential and logarithmic nonlinearity

Abstract In this paper, a p-Laplacian type pseudo-parabolic equation with singular potential and logarithmic nonlinearity is considered and finite time blow-up of solutions is proved with initial data at arbitrarily high initial energy level. A new criterion for the solutions to blow up in finite time is established by using Gagliardo-Nirenberg's interpolation inequality and inverse Sobolev inequality. It is worthy to point out that the lifespan of the weak solutions is estimated from both above and below. From methods to results, we partially extend some results obtained in recent literatures. AMS Mathematics Subject Classification 2010: 35K55, 35B44.