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Characterization of polynomial decay rate for the solution of linear evolution equation

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 undounded 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 explnentially stable systems to obtain the decay rate, which is not available in the literature.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00129703
Contributor : Grégory Thureau Connect in order to contact the contributor
Submitted on : Thursday, February 8, 2007 - 3:00:24 PM
Last modification on : Monday, January 31, 2022 - 9:10:01 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 8:59:46 PM

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Zhyangyi Liu, Bopeng Rao. Characterization of polynomial decay rate for the solution of linear evolution equation. 2004. ⟨hal-00129703⟩

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