Global existence and blow-up of solutions to porous medium equation for Baouendi-Grushin operator

In this note, we show a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation related to Baouendi-Grushin operator. Our approach is based on the concavity argument and the Poincaré inequality for Baouendi-Grushin vector fields from [35], inspired by the recent works [28] and [29].