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...
| Main Authors: | , |
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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 |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023129?viewType=HTML |
| Summary: | 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. |
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| ISSN: | 2688-1594 |