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Exponential stability in linear viscoelasticity with almost flat memory kernels

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  • 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 $\mu$.

    Mathematics Subject Classification: Primary: 35B40, 45K05; Secondary: 45M10, 47D06.


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