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Research Article | Open Access

Asymptotics for fractional reaction diffusion equations in periodic media

Yu Wei, Yahan Wang, Huiqin Lu( )
School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China
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Abstract

In this paper, the Cauchy problem for a class of reaction diffusion equations are considered with nonlocal interactions in periodic media. First, we demonstrate the existence and uniqueness of solutions that are both positive and bounded for the stationary equation. Second, we derive results concerning the existence and uniqueness of solutions for the Cauchy problem by using the semigroup theory. Finally, we analyze the behavior of the solutions to the Cauchy problem for large times by using the comparison principle.

Keywords

generalized fractional Laplacianconvolutionsemigroup theoryasymptotics
CLC number: 35B40, 35K57, 35R11

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 3819-3835
DOI: 10.3934/math.2025177

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Cite this article:
Wei Y, Wang Y, Lu H. Asymptotics for fractional reaction diffusion equations in periodic media. AIMS Mathematics, 2025, 10(2): 3819-3835. https://doi.org/10.3934/math.2025177

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Received: 20 September 2024
Revised: 26 January 2025
Accepted: 10 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)