The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain

Yaning Li; Yuting Yang; Yaning Li; Yuting Yang

doi:10.3934/era.2023129

Electronic Research Archive

2023, Volume 31, Issue 5: 2555-2567. doi: 10.3934/era.2023129

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Research article

The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain

Yaning Li ^,,
Yuting Yang

College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China

Received: 04 January 2023 Revised: 22 February 2023 Accepted: 26 February 2023 Published: 06 March 2023

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.
- fractional pseudo-parabolic equation,
- critical exponent,
- global existence,
- blow-up
Citation: Yaning Li, Yuting Yang. The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain[J]. Electronic Research Archive, 2023, 31(5): 2555-2567. doi: 10.3934/era.2023129

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Abstract

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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