English

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}
}