Asymptotic profiles of positive periodic solutions for a class of reaction-diffusion equations

Chen, Xiaodan; Cui, Renhao; Zhao, Xiao-Qiang

doi:10.1090/proc/17246

Asymptotic profiles of positive periodic solutions for a class of reaction-diffusion equations
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by Xiaodan Chen, Renhao Cui and Xiao-Qiang Zhao;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/17246

Published electronically: June 26, 2025

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Abstract:

This paper is concerned with the asymptotic profiles of positive periodic solutions for a class of reaction-diffusion equations, in which the reaction functions have the linear and nonlinear components. By analyzing the sharp “blow-up” phenomenon of positive solutions for large linear component or small nonlinear component, we show that these two components have rather distinct impacts on the limiting profile of positive periodic solutions. Moreover, we investigate the combined influence of linear and nonlinear components on the asymptotic profiles of positive periodic solutions. It turns out that the linear component plays a dominant role.

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Asymptotic profiles of positive periodic solutions for a class of reaction-diffusion equations
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Abstract: