Asymptotics for fractional reaction diffusion equations in periodic media

Yu Wei; Yahan Wang; Huiqin Lu; Yu Wei; Yahan Wang; Huiqin Lu

doi:10.3934/math.2025177

AIMS Mathematics

2025, Volume 10, Issue 2: 3819-3835. doi: 10.3934/math.2025177

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Research article

Asymptotics for fractional reaction diffusion equations in periodic media

School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

Received: 20 September 2024 Revised: 26 January 2025 Accepted: 10 February 2025 Published: 25 February 2025
MSC : 35B40, 35K57, 35R11

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.
- generalized fractional Laplacian,
- convolution,
- semigroup theory,
- asymptotics
Citation: Yu Wei, Yahan Wang, Huiqin Lu. Asymptotics for fractional reaction diffusion equations in periodic media[J]. AIMS Mathematics, 2025, 10(2): 3819-3835. doi: 10.3934/math.2025177

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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.

References

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