Characterization of polynomial decay rate for the solution of linear evolution equation |
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| Authors: | Zhuangyi Liu Bopeng Rao |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, USA;(2) Institut de Recherche Mathématique Avancée, Université de Louis Pasteur de Strasbourg, 7 Rue René-Descartes, 67084 Strasbourg Cedex, France |
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| Abstract: | In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be unbounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not exponentially stable systems to obtain the decay rate, which is not available in the literature.Received: July 21, 2003 |
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| Keywords: | 47D06 35B40 |
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