Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups
Michael RuzhanskyDepartment of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, BelgiumBolys SabitbekAl-Farabi Kazakh National University, Almaty, KazakhstanBerikbol T. TorebekDepartment of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
2022en
ABI
Аннотация
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 Poincaré inequality, established in Ruzhansky and Suragan (J Differ Eq 262:1799–1821, 2017) for stratified groups.
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