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Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified Groups (2106.00406v2)
Published 1 Jun 2021 in math.AP
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.