Analysis on stability and non-existence of equilibrium for a general chemical reaction
This paper is concerned with a general chemical reaction model with respect to Neumann boundary condition. The stability of positive equilibrium and the non-existence of non-constant positive solution are discussed rigorously, respectively in Case 1: $f(u)>0$ and $f_u(u)<0$ for $u>0$ and Ca...
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5934 |
| _version_ | 1797830510308753408 |
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| author | Wenbin Yang Yan'e Wang |
| author_facet | Wenbin Yang Yan'e Wang |
| author_sort | Wenbin Yang |
| collection | DOAJ |
| description | This paper is concerned with a general chemical reaction model with respect to Neumann boundary condition. The stability of positive equilibrium and the non-existence of non-constant positive solution are discussed rigorously, respectively in Case 1: $f(u)>0$ and $f_u(u)<0$ for $u>0$ and Case 2: $f(0)=0$ and $f_u(u)>0$ for $u>0$. The techniques include the spectrum analysis of operators, the maximal principle, the upper and lower solution method and the implicit function theorem. |
| first_indexed | 2024-04-09T13:38:21Z |
| format | Article |
| id | doaj.art-6199db0737e44341ba285a5bed1f762a |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:21Z |
| publishDate | 2018-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6199db0737e44341ba285a5bed1f762a2023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-04-0120181711210.14232/ejqtde.2018.1.175934Analysis on stability and non-existence of equilibrium for a general chemical reactionWenbin Yang0Yan'e Wang1Xi'an University of Posts and Telecommunications, Xi’an, ChinaShaanxi Normal University, Xi’an, ChinaThis paper is concerned with a general chemical reaction model with respect to Neumann boundary condition. The stability of positive equilibrium and the non-existence of non-constant positive solution are discussed rigorously, respectively in Case 1: $f(u)>0$ and $f_u(u)<0$ for $u>0$ and Case 2: $f(0)=0$ and $f_u(u)>0$ for $u>0$. The techniques include the spectrum analysis of operators, the maximal principle, the upper and lower solution method and the implicit function theorem.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5934general chemical reactionreaction-diffusion equationsstabilitynon-existence |
| spellingShingle | Wenbin Yang Yan'e Wang Analysis on stability and non-existence of equilibrium for a general chemical reaction Electronic Journal of Qualitative Theory of Differential Equations general chemical reaction reaction-diffusion equations stability non-existence |
| title | Analysis on stability and non-existence of equilibrium for a general chemical reaction |
| title_full | Analysis on stability and non-existence of equilibrium for a general chemical reaction |
| title_fullStr | Analysis on stability and non-existence of equilibrium for a general chemical reaction |
| title_full_unstemmed | Analysis on stability and non-existence of equilibrium for a general chemical reaction |
| title_short | Analysis on stability and non-existence of equilibrium for a general chemical reaction |
| title_sort | analysis on stability and non existence of equilibrium for a general chemical reaction |
| topic | general chemical reaction reaction-diffusion equations stability non-existence |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5934 |
| work_keys_str_mv | AT wenbinyang analysisonstabilityandnonexistenceofequilibriumforageneralchemicalreaction AT yanewang analysisonstabilityandnonexistenceofequilibriumforageneralchemicalreaction |