Positivity and regularity of hyperbolic Volterra equations in Banach spaces
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 (*).
scientific article; zbMATH DE number 3983845
scientific article