Global existence and blow-up of solutions to porous medium equation for Baouendi-Grushin operator
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909208190910464 |
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| author | Dukenbayeva, Aishabibi |
| author_facet | Dukenbayeva, Aishabibi |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and blow-up of solutions to porous medium equation for Baouendi-Grushin operator Dukenbayeva, Aishabibi Analysis of PDEs 35K65, 35K91, 35B44, 35A01 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]. |
| title | Global existence and blow-up of solutions to porous medium equation for Baouendi-Grushin operator |
| topic | Analysis of PDEs 35K65, 35K91, 35B44, 35A01 |
| url | https://arxiv.org/abs/2405.13225 |