Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions
Analysis of PDEs
2024-04-22 v1
Abstract
In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular function, we provide a complete characterization of the parameter ranges such that coexisting solutions of the system do not exist under three boundary conditions. Then based on the maximum principle, a sufficient condition for the existence of constant coexisting solutions of the system under Neumann boundary conditions was derived.
Keywords
Cite
@article{arxiv.2404.12664,
title = {Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions},
author = {Ningning Zhu and Dongpo Hu and Huili Bi},
journal= {arXiv preprint arXiv:2404.12664},
year = {2024}
}