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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

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

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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