Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:03:36.379Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Partial differential equations Qualitative behavior

Published online by Cambridge University Press:  31 May 2017

Valeria Danese  and
Filippo Dell'Oro
Valeria Danese
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy (valeria.danese@polimi.it; filippo.delloro@polimi.it)
Filippo Dell'Oro
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy (valeria.danese@polimi.it; filippo.delloro@polimi.it)
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

memory kernelcontraction semigroupstabilityexponential stability

MSC classification

Secondary: 35B40: Asymptotic behavior of solutions 45K05: Integro-partial differential equations 45M10: Stability theory
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)