Abstract.
Decay properties in energy norm for solutions of a class of partial differential equations with memory are studied by means of frequency domain methods. Our results are optimal for this class, as we are able to characterize polynomial as well as exponential decay rates. The results apply to models for viscoelastic materials. An extension to a semilinearly perturbed problem is also included.
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Received: 9 July 2008, Revised: 16 September 2008
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Prüss, J. Decay properties for the solutions of a partial differential equation with memory. Arch. Math. 92, 158–173 (2009). https://doi.org/10.1007/s00013-008-2936-x
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DOI: https://doi.org/10.1007/s00013-008-2936-x