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Existence and regularity for a class of integrodifferential equations of parabolic type. (English) Zbl 0583.45009

The authors investigate by Laplace transform methods the integrodifferential equation \(u'(t)=Au(t)+\int^{t}_{0}K(t- s)Au(s)ds+f(t)\) where A is the generator of an analytic semigroup in a Banach space X and f:[0,T]\(\to X\), K:[0,T]\(\to {\mathbb{R}}\) are given. The existence of a weak, strong and strict solution for the Cauchy problem is obtained together with an application to a parabolic partial integrodifferential equation.
Reviewer: G.Di Blasio

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45K05 Integro-partial differential equations
47D03 Groups and semigroups of linear operators
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