Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds
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 l...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-11-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2023-0117 |
| _version_ | 1797405211850964992 |
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| author | Chen Yuxuan |
| author_facet | Chen Yuxuan |
| author_sort | Chen Yuxuan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T03:06:32Z |
| format | Article |
| id | doaj.art-f3f6f72dfc3c4c29816a1b026905f972 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-03-09T03:06:32Z |
| publishDate | 2023-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-f3f6f72dfc3c4c29816a1b026905f9722023-12-04T07:59:10ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2023-11-01121pp. 14310.1515/anona-2023-0117Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifoldsChen Yuxuan0Engineering Research Center of Agricultural Microbiology Technology, Ministry of Education & Heilongjiang Provincial Key Laboratory of Ecological Restoration and Resource Utilization for Cold Region & School of Mathematical Sciences, Heilongjiang University, Harbin 150080, ChinaIn 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.https://doi.org/10.1515/anona-2023-0117global existencefinite-time blowupnonlinear parabolic equationsingular manifolds35k2035k55 |
| spellingShingle | Chen Yuxuan Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds Advances in Nonlinear Analysis global existence finite-time blowup nonlinear parabolic equation singular manifolds 35k20 35k55 |
| title | Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds |
| title_full | Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds |
| title_fullStr | Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds |
| title_full_unstemmed | Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds |
| title_short | Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds |
| title_sort | global well posedness for the semilinear edge degenerate parabolic equations on singular manifolds |
| topic | global existence finite-time blowup nonlinear parabolic equation singular manifolds 35k20 35k55 |
| url | https://doi.org/10.1515/anona-2023-0117 |
| work_keys_str_mv | AT chenyuxuan globalwellposednessforthesemilinearedgedegenerateparabolicequationsonsingularmanifolds |