Notes on spectrum and exponential decay in nonautonomous evolutionary equations
We first determine the dichotomy (Sacker-Sell) spectrum for certain nonautonomous linear evolutionary equations induced by a class of parabolic PDE systems. Having this information at hand, we underline the applicability of our second result: If the widths of the gaps in the dichotomy spectrum are b...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-08-01
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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=4202 |
| _version_ | 1797830552506597376 |
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| author | Christian Pötzsche Evamaria Russ |
| author_facet | Christian Pötzsche Evamaria Russ |
| author_sort | Christian Pötzsche |
| collection | DOAJ |
| description | We first determine the dichotomy (Sacker-Sell) spectrum for certain nonautonomous linear evolutionary equations induced by a class of parabolic PDE systems. Having this information at hand, we underline the applicability of our second result: If the widths of the gaps in the dichotomy spectrum are bounded away from $0$, then one can rule out the existence of super-exponentially decaying (i.e. slow) solutions of semi-linear evolutionary equations. |
| first_indexed | 2024-04-09T13:37:55Z |
| format | Article |
| id | doaj.art-035ceabdc24446319233fa2e8f63ad79 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:55Z |
| publishDate | 2016-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-035ceabdc24446319233fa2e8f63ad792023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-08-0120161911510.14232/ejqtde.2016.8.194202Notes on spectrum and exponential decay in nonautonomous evolutionary equationsChristian Pötzsche0Evamaria Russ1Institut für Mathematik, Alpen-Adria Universität Klagenfurt, AustriaInstitut für Mathematik, Alpen-Adria Universität Klagenfurt, AustriaWe first determine the dichotomy (Sacker-Sell) spectrum for certain nonautonomous linear evolutionary equations induced by a class of parabolic PDE systems. Having this information at hand, we underline the applicability of our second result: If the widths of the gaps in the dichotomy spectrum are bounded away from $0$, then one can rule out the existence of super-exponentially decaying (i.e. slow) solutions of semi-linear evolutionary equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4202nonautonomous evolutionary equationdichotomy spectrumsacker-sell spectrumslow solutions |
| spellingShingle | Christian Pötzsche Evamaria Russ Notes on spectrum and exponential decay in nonautonomous evolutionary equations Electronic Journal of Qualitative Theory of Differential Equations nonautonomous evolutionary equation dichotomy spectrum sacker-sell spectrum slow solutions |
| title | Notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| title_full | Notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| title_fullStr | Notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| title_full_unstemmed | Notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| title_short | Notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| title_sort | notes on spectrum and exponential decay in nonautonomous evolutionary equations |
| topic | nonautonomous evolutionary equation dichotomy spectrum sacker-sell spectrum slow solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4202 |
| work_keys_str_mv | AT christianpotzsche notesonspectrumandexponentialdecayinnonautonomousevolutionaryequations AT evamariaruss notesonspectrumandexponentialdecayinnonautonomousevolutionaryequations |