Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source
A $p$-Laplacian parabolic equation with a general nonlinear source term is considered. It is shown that the solution may blow up in finite time at positive initial energy. Moreover, under some suitable assumptions about the nonlinear source term, the solution is proved to blow up in finite time at a...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-04-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.248/ |
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| _version_ | 1825205955897327616 |
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| author | Ding, Hang Zhou, Jun |
| author_facet | Ding, Hang Zhou, Jun |
| author_sort | Ding, Hang |
| collection | DOAJ |
| description | A $p$-Laplacian parabolic equation with a general nonlinear source term is considered. It is shown that the solution may blow up in finite time at positive initial energy. Moreover, under some suitable assumptions about the nonlinear source term, the solution is proved to blow up in finite time at arbitrarily high initial energy. These results generalize the previous ones. |
| format | Article |
| id | doaj-art-c2e0f19fcff04f0b9b0ab34dd702c5ac |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-c2e0f19fcff04f0b9b0ab34dd702c5ac2025-02-07T13:48:46ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-04-01352G1718010.5802/crmeca.24810.5802/crmeca.248Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear sourceDing, Hang0Zhou, Jun1School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R.ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R.ChinaA $p$-Laplacian parabolic equation with a general nonlinear source term is considered. It is shown that the solution may blow up in finite time at positive initial energy. Moreover, under some suitable assumptions about the nonlinear source term, the solution is proved to blow up in finite time at arbitrarily high initial energy. These results generalize the previous ones.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.248/$p$-Laplacian parabolic equationgeneral nonlinear source termblow-up |
| spellingShingle | Ding, Hang Zhou, Jun Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source Comptes Rendus. Mécanique $p$-Laplacian parabolic equation general nonlinear source term blow-up |
| title | Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source |
| title_full | Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source |
| title_fullStr | Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source |
| title_full_unstemmed | Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source |
| title_short | Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source |
| title_sort | blow up to a p laplacian parabolic equation with a general nonlinear source |
| topic | $p$-Laplacian parabolic equation general nonlinear source term blow-up |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.248/ |
| work_keys_str_mv | AT dinghang blowuptoaplaplacianparabolicequationwithageneralnonlinearsource AT zhoujun blowuptoaplaplacianparabolicequationwithageneralnonlinearsource |