Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929320624128000 |
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| author | Zhu, Ningning Hu, Dongpo Bi, Huili |
| author_facet | Zhu, Ningning Hu, Dongpo Bi, Huili |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions Zhu, Ningning Hu, Dongpo Bi, Huili Analysis of PDEs 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. |
| title | Coexisting steady-state solutions of a class of reaction-diffusion systems with different boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.12664 |