Conditional stability and periodicity of solutions to evolution equations (Q2064537)
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scientific article; zbMATH DE number 7452664
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Conditional stability and periodicity of solutions to evolution equations |
scientific article; zbMATH DE number 7452664 |
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Conditional stability and periodicity of solutions to evolution equations (English)
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6 January 2022
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The authors first prove the existence and uniqueness of periodic mild solutions to a first-order linear nonautonomous differential equation in a Banach space. The key assumption is that the time dependent linear operators governing the equation generate a strongly continuous, exponentially bounded evolution family. A related semilinear evolution equation is next considered. Finally, applications of the theory to exponentially dichotomic evolution families, and nonautonomous damped wave equations are given.
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evolution families
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conditional \(\varphi\)-stability
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periodic solutions
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exponential dichotomy
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nonautonomous damped wave equations
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