| Autor: |
Luong, Vu Trong, Barker, William, Huy, Nguyen Duc, Van Minh, Nguyen |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study the existence of bounded asymptotic mild solutions to evolution equations of the form $u'(t)=Au(t)+f(t), t\ge 0$ in a Banach space $\X$, where $A$ generates an (analytic) $C_0$-semigroup and $f$ is bounded. We find spectral conditions on $A$ and $f$ for the existence and uniqueness of asymptotic mild solutions with the same "profile" as that of $f$. In the resonance case, a sufficient condition of Massera type theorem is found for the existence of bounded solutions with the same profile as $f$. The obtained results are stated in terms of spectral properties of $A$ and $f$, and they are analogs of classical results of Katznelson-Tzafriri and Massera for the evolution equations on the half line. Applications from PDE are given. |
| Databáze: |
arXiv |
| Externí odkaz: |
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