Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds
Abstract: In this article, we study the long-time dynamical behavior of the solution for a class of semilinear edge-degenerate parabolic equations on manifolds with edge singularities. By introducing a family of potential well and compactness method, we reveal the dependence between the initial data and the long-time dynamical behavior of the solution. Specifically, we give the threshold condition for the initial data, which makes the solution exist globally or blowup in finite-time with subcritical, critical, and supercritical initial energy, respectively. Moreover, we also discussed the long-time behavior of the global solution, the estimate of blowup time, and blowup rate. Our results show that the relationship between the initial data and the long-time behavior of the solution can be revealed in the weighted Sobolev spaces for nonlinear parabolic equations on manifolds with edge singularities.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds ; volume:12 ; number:1 ; year:2023 ; extent:36
Advances in nonlinear analysis ; 12, Heft 1 (2023) (gesamt 36)
- Creator
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Chen, Yuxuan
- DOI
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10.1515/anona-2023-0117
- URN
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urn:nbn:de:101:1-2023112913330225081032
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:36 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Chen, Yuxuan
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