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Positivity and regularity of hyperbolic Volterra equations in Banach spaces. (English) Zbl 0608.45007
We derive necessary and sufficient conditions for two classes of linear Volterra equations of the form (*) $u=f+a*Au$ to admit finite wave speed as well as continuity across the wave front. These conditions are based on the positivity of the fundamental solution. One of these classes serves as a model in linear viscoelasticity. These results are then used to obtain several general theorems on existence, positivity, regularity and asymptotic behavior of the resolvent for (*).

MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces 45M05 Asymptotic theory of integral equations 74D99 Materials of strain-rate type and history type, other materials with memory
References:
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