In this work, we aim to obtain the existence and finite time blow up of weak solutions of a p(x) -Laplacian pseudo-parabolic equation with memory term and logarithmic nonlinearity. Moreover, we extract an upper bound for the blow up time by applying the concavity method and a lower bound using the differential inequality technique.

In this paper, we establish existence and finite time blow up of weak solutions of a parabolic equation of p(x)-Laplacian type with the Dirichlet boundary condition. Moreover, we obtain upper and lower bounds for the blow up time of solutions, by employing concavity method and differential inequality technique respectively.