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memory kernel

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

The lack of exponential stability for a class of second-order systems with memory
Part of
- Partial differential equations
- Qualitative behavior
Valeria Danese, Filippo Dell'Oro
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 4 / August 2017

Published online by Cambridge University Press:

31 May 2017, pp. 683-702

Print publication:

August 2017
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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.