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On linear Volterra equations of parabolic type in Banach spaces

Author: Jan Prüss
Journal: Trans. Amer. Math. Soc. 301 (1987), 691-721
MSC: Primary 45N05; Secondary 45D05, 45K05, 47D05
MathSciNet review: 882711
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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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Keywords: Analytic semigroup, Laplace transform, maximal regularity, resolvent operator, resolvent equations, Volterra operator
Article copyright: © Copyright 1987 American Mathematical Society

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