Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator
In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity argument and the Poincaré inequality related to the Baouendi-Grus...
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| Language: | English |
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De Gruyter
2025-05-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0144 |
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| author | Dukenbayeva Aishabibi |
| author_facet | Dukenbayeva Aishabibi |
| author_sort | Dukenbayeva Aishabibi |
| collection | DOAJ |
| description | In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity argument and the Poincaré inequality related to the Baouendi-Grushin operator from [Suragan and Yessirkegenov, Sharp remainder of the Poincaré inequality for Baouendi–Grushin vector fields, Asian-Eur. J. Math. 16 (2023), 2350041], inspired by the recent work [Ruzhansky et al., Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified group, Manuscripta Math. 171 (2023), 377–395]. |
| format | Article |
| id | doaj-art-375fed3b7e6b4099a9b14b10ee0fc274 |
| institution | OA Journals |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-375fed3b7e6b4099a9b14b10ee0fc2742025-08-20T02:38:52ZengDe GruyterOpen Mathematics2391-54552025-05-0123161462710.1515/math-2025-0144Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operatorDukenbayeva Aishabibi0KIMEP University, Almaty, KazakhstanIn this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity argument and the Poincaré inequality related to the Baouendi-Grushin operator from [Suragan and Yessirkegenov, Sharp remainder of the Poincaré inequality for Baouendi–Grushin vector fields, Asian-Eur. J. Math. 16 (2023), 2350041], inspired by the recent work [Ruzhansky et al., Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified group, Manuscripta Math. 171 (2023), 377–395].https://doi.org/10.1515/math-2025-0144blow-upglobal solutionpseudo-parabolic equationbaouendi-grushin operator35k6535k9135b4435a01 |
| spellingShingle | Dukenbayeva Aishabibi Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator Open Mathematics blow-up global solution pseudo-parabolic equation baouendi-grushin operator 35k65 35k91 35b44 35a01 |
| title | Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator |
| title_full | Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator |
| title_fullStr | Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator |
| title_full_unstemmed | Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator |
| title_short | Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator |
| title_sort | global existence and blow up of solutions to pseudo parabolic equation for baouendi grushin operator |
| topic | blow-up global solution pseudo-parabolic equation baouendi-grushin operator 35k65 35k91 35b44 35a01 |
| url | https://doi.org/10.1515/math-2025-0144 |
| work_keys_str_mv | AT dukenbayevaaishabibi globalexistenceandblowupofsolutionstopseudoparabolicequationforbaouendigrushinoperator |