Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry
Analysis of PDEs
2024-09-10 v1
Abstract
In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in the elliptic space. Then, we establish crucial principles, including the asymptotic narrow region principle.Finally, we employ the method of moving planes to demonstrate the asymptotic symmetry of the solutions.
Keywords
Cite
@article{arxiv.2409.05366,
title = {Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry},
author = {Baiyu Liu and Wenlong Yang},
journal= {arXiv preprint arXiv:2409.05366},
year = {2024}
}