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Research Article | Open Access

Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry

Baiyu Liu( ), Wenlong Yang
School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District Beijing, 100083, P.R. China
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Abstract

In this paper, we investigated the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. First, we discussed the properties of solutions in the elliptic space. Then, we established crucial principles, including the asymptotic narrow region principle. Finally, we employed the method of moving planes to demonstrate the asymptotic symmetry of the solutions.

Keywords

parabolic equationasymptotic symmetrymonotonicityelliptic geometry
CLC number: 35R11, 35B07

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Communications in Analysis and Mechanics
Volume 17 Issue 2,
June 2025
Pages 341-364
DOI: 10.3934/cam.2025014

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Liu B, Yang W. Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry. Communications in Analysis and Mechanics, 2025, 17(2): 341-364. https://doi.org/10.3934/cam.2025014

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Received: 15 September 2024
Revised: 12 March 2025
Accepted: 18 March 2025
Published: 09 April 2025
©2025 the Author(s), licensee AIMS Press.

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