Article
| Title: | Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space (English) |
| Author: | Gil', Michael |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 355-366 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We consider the equation ${\rm d}y(t)/{\rm d}t=(A+B(t))y(t)$ $(t\ge 0)$, where $A$ is the generator of an analytic semigroup $({\rm e}^{At})_{t\ge 0}$ on a Banach space ${\cal X}$, $B(t)$ is a variable bounded operator in ${\cal X}$. It is assumed that the commutator $K(t)=AB(t)-B(t)A$ has the following property: there is a linear operator $S$ having a bounded left-inverse operator $S_l^{-1}$ such that $\|S {\rm e}^{At}\|$ is integrable and the operator $K(t)S_l^{-1}$ is bounded. Under these conditions an exponential stability test is derived. As an example we consider a coupled system of parabolic equations. (English) |
| Keyword: | Banach space |
| Keyword: | differential equation |
| Keyword: | linear nonautonomous equation |
| Keyword: | exponential stability |
| Keyword: | commutator |
| Keyword: | parabolic equation |
| MSC: | 34G10 |
| MSC: | 35B35 |
| MSC: | 35K51 |
| MSC: | 47D06 |
| idZBL: | Zbl 07729512 |
| idMR: | MR4586899 |
| DOI: | 10.21136/CMJ.2023.0188-21 |
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| Date available: | 2023-05-04T17:42:10Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151662 |
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