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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Remarks on the asymptotic behavior of solutions to damped evolution equations in Hilbert space


Author: Frederick Bloom
Journal: Proc. Amer. Math. Soc. 75 (1979), 25-31
MSC: Primary 34G10; Secondary 35B40
DOI: https://doi.org/10.1090/S0002-9939-1979-0529206-7
MathSciNet review: 529206
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Abstract: Lower bounds are derived for the norms of solutions to a class of intitial-value problems associated with the damped evolution equation $ {u_{tt}} + A{u_t} + Bu = 0$ in Hilbert space. Under appropriate assumptions on the linear operator B it is shown that even in the special strongly damped case where $ A = \Gamma I,\Gamma > 0$, solutions are bounded away from zero as $ t \to + \infty $, even when $ \Gamma \to + \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0529206-7
Article copyright: © Copyright 1979 American Mathematical Society