  In this article, we consider a semilinear pseudo parabolic heat equation with
the nonlinearity which is the product of logarithmic and polynomial functions.
Here we prove the global existence of solution to the problem for arbitrary
dimension $n \geq 1$ and power index $p>1$. Asymptotic behaviour of the
solution has been addressed at different energy levels. Moreover, we prove that
the global solution indeed decays with an exponential rate. Finally, sufficient
conditions are provided under which blow up of solutions take place.
