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Zbl 0608.45007
Prüss, Jan
Positivity and regularity of hyperbolic Volterra equations in Banach spaces. (English)
[J] Math. Ann. 279, No. 1-2, 317-344 (1987). ISSN 0025-5831; ISSN 1432-1807/e

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 2000:: *45N05 Integral equations in abstract spaces
45M05 Asymptotic theory of integral equations
74D99 Materials of strain-rate type and history type, etc.

Keywords: hyperbolic Volterra equations; Banach spaces; linear viscoelasticity; existence; positivity; regularity; asymptotic behavior; resolvent

Cited in: Zbl 1166.65401 Zbl 0858.73027 Zbl 0685.93006 Zbl 0647.45012

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