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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 $u'(t)=Au(t)+\int\sp{t}\sb{0}K(t- s)Au(s)ds+f(t)$ where A is the generator of an analytic semigroup in a Banach space X and f:[0,T]$\to X$, K:[0,T]$\to {\bbfR}$ 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:
45N05Abstract integral equations, integral equations in abstract spaces
45K05Integro-partial differential equations
47D03(Semi)groups of linear operators
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References:
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