Radial symmetry, monotonicity and Liouville theorem for Marchaud fractional parabolic equations with the nonlocal Bellman operator
In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs ${\partial }_{t}^{\alpha }-{F}_{s}$ , we first establish the n...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-06-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0191 |
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| Summary: | In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs
${\partial }_{t}^{\alpha }-{F}_{s}$
, we first establish the narrow region principle and the maximum principle. Next, we establish a direct method of moving planes applicable to the operator ∂tα−Fs
${\partial }_{t}^{\alpha }-{F}_{s}$
. Finally, combining perturbation techniques and limit arguments, we apply this direct method of moving planes to prove the radial symmetry and monotonicity of solutions for the space-time fractional parabolic equations involving the nonlocal Bellman operator and the Marchaud fractional derivative. Additionally, the Liouville theorem of homogeneous space-time fractional parabolic equation is proved. |
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| ISSN: | 2169-0375 |