Existence and blow-up of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity

Abstract In this paper, we prove the existence of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity in an interval $[0, T)$ [ 0 , T ) by employing the Galerkin approximation method and compactness arguments. We show that the solutions become unbounded at a finite time $T^{\star}$ T ⋆ and find upper and lower bounds for this time.