Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting
In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0 (t real) where the operators A_t periodically depend on t and the function u takes values in a UMD Banach space X.We impose a suitable condition on the operator family (A_t) and their common domain, in pa...
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| Formato: | Online |
| Idioma: | inglês |
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KIT Scientific Publishing
2021
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| Acesso em linha: | 34418 |
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| _version_ | 1869516876391907328 |
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| author | Gauss, Thomas |
| author_browse | Gauss, Thomas |
| author_facet | Gauss, Thomas |
| author_sort | Gauss, Thomas |
| collection | Directory of Open Access Books |
| description | In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0 (t real) where the operators A_t periodically depend on t and the function u takes values in a UMD Banach space X.We impose a suitable condition on the operator family (A_t) and their common domain, in particular a decay condition for certain resolvents, to obtain the central result that all exponentially bounded solutions can be described as a superposition of a fixed family of Floquet solutions. |
| format | Online |
| id | doab-20.500.12854ir-47753 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | KIT Scientific Publishing |
| publisherStr | KIT Scientific Publishing |
| record_format | ojs |
| spelling | doab-20.500.12854ir-477532023-12-20T18:40:43Z Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting Gauss, Thomas QA75.5-76.95 Bloch solution Lp setting Floquet theory periodic evolution equation superposition principle bic Book Industry Communication::U Computing & information technology::UY Computer science In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0 (t real) where the operators A_t periodically depend on t and the function u takes values in a UMD Banach space X.We impose a suitable condition on the operator family (A_t) and their common domain, in particular a decay condition for certain resolvents, to obtain the central result that all exponentially bounded solutions can be described as a superposition of a fixed family of Floquet solutions. 2021-02-11T13:47:13Z 2021-02-11T13:47:13Z 2019-07-30 20:01:57 2010 book 34418 9783866445420 https://directory.doabooks.org/handle/20.500.12854/47753 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.ksp.kit.edu/9783866445420 KIT Scientific Publishing 10.5445/KSP/1000019300 10.5445/KSP/1000019300 68fffc18-8f7b-44fa-ac7e-0b7d7d979bd2 9783866445420 IV, 130 p. open access |
| spellingShingle | QA75.5-76.95 Bloch solution Lp setting Floquet theory periodic evolution equation superposition principle bic Book Industry Communication::U Computing & information technology::UY Computer science Gauss, Thomas Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title | Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title_full | Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title_fullStr | Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title_full_unstemmed | Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title_short | Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting |
| title_sort | floquet theory for a class of periodic evolution equations in an lp setting |
| topic | QA75.5-76.95 Bloch solution Lp setting Floquet theory periodic evolution equation superposition principle bic Book Industry Communication::U Computing & information technology::UY Computer science |
| topic_facet | QA75.5-76.95 Bloch solution Lp setting Floquet theory periodic evolution equation superposition principle bic Book Industry Communication::U Computing & information technology::UY Computer science |
| url | 34418 |
| work_keys_str_mv | AT gaussthomas floquettheoryforaclassofperiodicevolutionequationsinanlpsetting |