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 f...

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Author: Dukenbayeva, Aishabibi
Format: Article
Language:English
Subjects:
Boundary value problems
Concavity
Fields (mathematics)
Porous media
Online Access:Get full text
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Summary: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].
ISSN:2331-8422