Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations
2013 ◽
Vol 2013
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pp. 1-5
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Keyword(s):
Let be a generator of an exponentially stable operator semigroup in a Banach space, and let be a linear bounded variable operator. Assuming that is sufficiently small in a certain sense for the equation , we derive exponential stability conditions. Besides, we do not require that for each , the “frozen” autonomous equation is stable. In particular, we consider evolution equations with periodic operator coefficients. These results are applied to partial differential equations.
1999 ◽
Vol 60
(2)
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pp. 319-330
2020 ◽
Vol 5
(1)
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pp. 249-254
1993 ◽
Vol 336
(2)
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pp. 523
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2017 ◽
Vol 14
(04)
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pp. 1750041
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2008 ◽
Vol 196
(917)
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pp. 0-0
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