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

Abstract 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 [Suragan and Yessirkegenov, Sharp remainder of the Poincaré inequality for Baouendi–Grushin vector fields , Asian-Eur. J. Math. 16 (2023), 2350041], inspired by the recent work [Ruzhansky et al., Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified group , Manuscripta Math. 171 (2023), 377–395].