A Semigroup Method for Delay Equations with Relatively Bounded Operators in the Delay Term |
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| Authors: | András Bátkai and Susanna Piazzera |
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| Affiliation: | (1) ELTE TTK Department of Applied Analysis Kecskeméti u. 10-12 1053 Budapest, Hungary batka@cs.elte.hu, HU;(2) Mathematisches Institut Universit?t Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany supi@michelangelo.mathematik.uni-tuebingen.de, DE;(3) Abteilung Angewandte Analysis Universit?t Ulm 89069 Ulm, Germany piazzera@mathematik.uni-ulm.de, DE |
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| 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. September 12, 2000 |
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