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

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arxiv 2405.13225 v1 pith:XV227EKK submitted 2024-05-21 math.AP

Aishabibi Dukenbayeva This is my paper · ORCID
classification math.AP
keywords baouendi-grushinblow-upequationexistenceglobalmediumoperatorporous
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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 Poincar\'e inequality for Baouendi-Grushin vector fields from [35], inspired by the recent works [28] and [29].

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  1. Sharp remainder of the $L^{p}$-Poincar\'e inequality for Baouendi-Grushin vector fields

    math.AP 2025-07 reject novelty 3.0 of 10

    An attempted Lp sharp remainder formula for the Baouendi-Grushin Poincaré inequality and a PME application, but the complex-valued formulation is incorrect.

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