Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator

In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity argument and the Poincaré inequality related to the Baouendi-Grushin operator from [24], inspired by the recent work [21].