The lack of exponential stability for a class of second-order systems with memory

We analyse the decay properties of the solution semigroup S(t) generated by the linear integrodifferential equation where the operator A is strictly positive self-adjoint with A –1 not necessarily compact. The asymptotic stability of S(t) is investigated in terms of the dependence of the parameter γ...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 147; no. 4; pp. 683 - 702
Main Authors Danese, Valeria, Dell'Oro, Filippo
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.08.2017
Cambridge University Press
Subjects
Asymptotic properties
Computer memory
Stability analysis
Systems analysis
contraction semigroup
47D05
Primary 35B40
45K05
45M10
memory kernel
stability
exponential stability
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ISSN0308-2105
1473-7124
DOI10.1017/S0308210516000330

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Summary:We analyse the decay properties of the solution semigroup S(t) generated by the linear integrodifferential equation where the operator A is strictly positive self-adjoint with A –1 not necessarily compact. The asymptotic stability of S(t) is investigated in terms of the dependence of the parameter γ ∈ ℝ. In particular, we show that S(t) is not exponentially stable when γ ≠ 1.
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ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210516000330