Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions

Ningning Zhu; Dongpo Hu; Huili Bi

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arXiv · 2404.12664

Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions

Ningning Zhu·Dongpo Hu·Huili Bi

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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.

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Ningning Zhu, Dongpo Hu, Huili Bi. 2024-04-19. Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions. https://arxiv.org/abs/2404.12664

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