On linear Volterra equations of parabolic type in Banach spaces

Prüss, Jan

doi:10.1090/S0002-9947-1987-0882711-5

On linear Volterra equations of parabolic type in Banach spaces
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Trans. Amer. Math. Soc. 301 (1987), 691-721 Request permission

Abstract:

Linear integrodifferential equations of Volterra type in a Banach space are studied in case the main part of the equation generates an analytic ${C_0}$-semigroup. Under very general assumptions it is shown that a resolvent operator exists and that many of the solution properties of parabolic evolution equations are inherited. The results are then applied to integro-partial differential equations of parabolic type.

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The Laplace transform