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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)+ 0 t 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]X, K:[0,T] 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
45N05Abstract integral equations, integral equations in abstract spaces
45K05Integro-partial differential equations
47D03(Semi)groups of linear operators