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May  2010, 9(3): 721-730. doi: 10.3934/cpaa.2010.9.721

Exponential stability in linear viscoelasticity with almost flat memory kernels

1. 

Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received  April 2009 Revised  August 2009 Published  January 2010

This article is focused on the solution semigroup in the history space framework arising from an abstract version of the boundary value problem with memory

$\partial_{t t} u(t)-\Delta [u(t)+\int_0^\infty \mu(s)[u(t)-u(t-s)] ds ]=0,\quad u(t)_{|\partial\Omega}=0,$

modelling linear viscoelasticity. The exponential stability of the semigroup is discussed, establishing a necessary and sufficient condition involving the memory kernel $\mu$.

Citation: Vittorino Pata. Exponential stability in linear viscoelasticity with almost flat memory kernels. Communications on Pure & Applied Analysis, 2010, 9 (3) : 721-730. doi: 10.3934/cpaa.2010.9.721
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