@article{Wei2025, 
author = {Yu Wei and Yahan Wang and Huiqin Lu},
title = {Asymptotics for fractional reaction diffusion equations in periodic media},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {3819-3835},
keywords = {generalized fractional Laplacian, convolution, semigroup theory, asymptotics},
url = {https://www.sciopen.com/article/10.3934/math.2025177},
doi = {10.3934/math.2025177},
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.}
}