Blow-up Phenomena for a Pseudo-parabolic Equation on Stratified Groups

In the present work, the blow-up of the solution of a pseudo-parabolic equation is studied on the stratified groups. To prove our results we use the method of concavity. First, we show the upper bound of the blow-up time of the solution with nonpositive energy. Then, we show that there is no global in-time solution with positive energy under some conditions to the initial value.