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

Baiyu Liu; Wenlong Yang

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arXiv · 2409.05366

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

Baiyu Liu·Wenlong Yang

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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.

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Baiyu Liu, Wenlong Yang. 2024-09-09. Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry. https://arxiv.org/abs/2409.05366

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