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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 1, Pages 48–69 (Mi vyuru358)  

Mathematical Modelling

Regularity results and solution semigroups for retarded functional differential equations

A. Favinia, H. Tanabeb

a Department of Mathematics, University of Bologna, Bologna, Italy
b Takarazuka, Japan

Abstract: We show that the solutions of the retarded functional differential equations in a Banach space, whose existence and uniqueness are established in paper of A. Favini and H. Tanabe, have some further regularity properties if the initial data and the inhomogeneous term satisfy some smootheness assumptions. Some results on the solution semigroups analogous to the one of G. Di Blasio, K. Kunisch and E. Sinestrari and to the one of E. Sinestrari are also obtained.

Keywords: retarded functional differential equation; regularity of solutions; analytic semigroup; solution semigroup; $C_0$-semigroup; infinitesimal generator.

DOI: https://doi.org/10.14529/mmp170104

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Bibliographic databases:

UDC: 517.9
MSC: 45K05, 47D06, 34K30
Received: 28.11.2016
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Citation: A. Favini, H. Tanabe, “Regularity results and solution semigroups for retarded functional differential equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:1 (2017), 48–69

Citation in format AMSBIB
\Bibitem{FavTan17}
\by A.~Favini, H.~Tanabe
\paper Regularity results and solution semigroups for retarded functional differential equations
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 1
\pages 48--69
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\crossref{https://doi.org/10.14529/mmp170104}
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\elib{https://elibrary.ru/item.asp?id=28922151}


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