Blow-up for a pseudo-parabolic $ p $-Kirchhoff equation with logarithmic nonlinearity

Abstract

In this paper, an initial boundary value problem for a pseudo-parabolic type $ p $-Kirchhoff equation with logarithmic nonlinearity is investigated. By proving the invariance of the unstable set under the semi-flow of this problem and adopting the Levine's concavity argument, a general finite time blow-up criterion for this problem is established, which in particular implies that for some initial data, the problem admits finite time blow-up solutions at arbitrarily high initial energy level. Moreover, the lifespan of the blow-up solutions is estimated from above.