Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified Groups

Abstract

In this paper, we prove a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation and the nonlinear pseudo-parabolic equation on the stratified Lie groups. Our proof is based on the concavity argument and the Poincar\'e inequality, established in [38] for stratified groups.