The lack of exponential stability for a class of second-order systems with memory
Published online by Cambridge University Press: 31 May 2017
Extract
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 4 , August 2017 , pp. 683 - 702
- Copyright
- Copyright © Royal Society of Edinburgh 2017
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