Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations
Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have t...
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| Format: | Article |
| Language: | English |
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University of Szeged
2000-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=47 |
| _version_ | 1827951430144622592 |
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| author | P. Polacik E. Yanagida |
| author_facet | P. Polacik E. Yanagida |
| author_sort | P. Polacik |
| collection | DOAJ |
| description | Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions). The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex) domains. |
| first_indexed | 2024-04-09T13:42:41Z |
| format | Article |
| id | doaj.art-7106c741eae1480aa9da90289dce4ff3 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:41Z |
| publishDate | 2000-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-7106c741eae1480aa9da90289dce4ff32023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752000-01-0119992211010.14232/ejqtde.1999.5.2247Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equationsP. Polacik0E. Yanagida1Comenius University, Bratislava, SlovakiaUniversity of Tokyo, JapanTime-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions). The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex) domains.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=47 |
| spellingShingle | P. Polacik E. Yanagida Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations |
| title_full | Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations |
| title_fullStr | Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations |
| title_full_unstemmed | Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations |
| title_short | Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations |
| title_sort | stable subharmonic solutions and asymptotic behavior in reaction diffusion equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=47 |
| work_keys_str_mv | AT ppolacik stablesubharmonicsolutionsandasymptoticbehaviorinreactiondiffusionequations AT eyanagida stablesubharmonicsolutionsandasymptoticbehaviorinreactiondiffusionequations |