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

Bloom, Frederick

doi:10.1090/S0002-9939-1979-0529206-7

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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