A blow-up criterion for a p-Laplacian-type pseudo-parabolic equation involving singular potential and logarithmic source

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Abstract

The main goal of this paper was to develop new skills to investigate the blow-up properties of solutions to an initial-boundary value problem for a p-Laplacian-type pseudo-parabolic equation with singular potential and logarithmic source. By establishing a crucial reverse Sobolev inequality, we derived that the solutions blow up in finite time under a new blow-up criterion and we estimated the lifespan of the weak solutions from both above and below. It is worthy to point out that our blow-up criterion implies that this problem admits finite time blow-up solutions at an arbitrarily high initial energy level. From methods to results, we partially extended some results obtained in recent literatures.

Keywords

pseudo-parabolic equation / p-Laplacian / singular potential / logarithmic nonlinearity / arbitrarily high initial energy / blow-up / lifespan

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