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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| Format: | Online |
| Idioma: | anglès |
| Publicat: |
KIT Scientific Publishing
2021
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| Matèries: | |
| Accés en línia: | 34418 |
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| Sumari: | 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. |
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