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A semigroup method for delay equations with relatively bounded operators in the delay term |
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| Authors: | András Bátkai Susanna Piazzera |
| Institution: | 1. Department of Applied Analysis, ELTE TTK, Kecskeméti u. 10-12, 1053, Budapest, Hungary 2. Mathematisches Institut, Universit?t Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany 3. Abteilung Angewandte Analysis, Universit?t Ulm, 89069, Ulm, Germany |
| Abstract: | We consider well-posedness and stability of abstract partial differential equations with unbounded operators in their delay terms. We show that the problem is equivalent to an abstract Cauchy problem in a product Banach space, give sufficient conditions on the well-posedness, make a complete spectral analysis and give robust stability criteria. The results are applied to the problem of small delays and to damped plate equations. |
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