The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain
This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ \alpha < \gamma $ and $ \alpha\ge \gamma, $ respectively. The result...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023129?viewType=HTML |
| _version_ | 1797831782334201856 |
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| author | Yaning Li Yuting Yang |
| author_facet | Yaning Li Yuting Yang |
| author_sort | Yaning Li |
| collection | DOAJ |
| description | This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ \alpha < \gamma $ and $ \alpha\ge \gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents. |
| first_indexed | 2024-04-09T13:58:18Z |
| format | Article |
| id | doaj.art-debbef3ee1354b4393b5c7358fa03f8c |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T13:58:18Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-debbef3ee1354b4393b5c7358fa03f8c2023-05-08T01:16:27ZengAIMS PressElectronic Research Archive2688-15942023-03-013152555256710.3934/era.2023129The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domainYaning Li 0Yuting Yang1College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, ChinaCollege of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, ChinaThis paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ \alpha < \gamma $ and $ \alpha\ge \gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents.https://www.aimspress.com/article/doi/10.3934/era.2023129?viewType=HTMLfractional pseudo-parabolic equationcritical exponentglobal existenceblow-up |
| spellingShingle | Yaning Li Yuting Yang The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain Electronic Research Archive fractional pseudo-parabolic equation critical exponent global existence blow-up |
| title | The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain |
| title_full | The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain |
| title_fullStr | The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain |
| title_full_unstemmed | The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain |
| title_short | The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain |
| title_sort | critical exponents for a semilinear fractional pseudo parabolic equation with nonlinear memory in a bounded domain |
| topic | fractional pseudo-parabolic equation critical exponent global existence blow-up |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023129?viewType=HTML |
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