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General decay properties of abstract linear viscoelasticity

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Abstract

We consider a linear Volterra integro-differential equation of hyperbolic type, which can be viewed as an abstract version of the equation

$$\begin{aligned} \partial _{tt} u(t)- \varDelta u(t) +\displaystyle \int \limits _0^t\mu (s)\varDelta u(t-s)\mathrm{d}s=0 \end{aligned}$$

describing the motion of linearly viscoelastic solids. We establish some decay results for the associated energy, under assumptions that do not involve differential inequalities for the convolution kernel \(\mu \).

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  1. Politecnico di Milano - Dipartimento di Matematica, Via Bonardi 9, 20133, Milan, Italy

    Monica Conti & Vittorino Pata

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  1. Monica Conti
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  2. Vittorino Pata
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Correspondence to Monica Conti.

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Conti, M., Pata, V. General decay properties of abstract linear viscoelasticity. Z. Angew. Math. Phys. 71, 6 (2020). https://doi.org/10.1007/s00033-019-1229-5

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