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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-05-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0144 |
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| Summary: | 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]. |
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| ISSN: | 2391-5455 |