Geodesic
Regularity results and solution semigroups for retarded functional differential equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 48-69

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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. 
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     author = {A. Favini and H. Tanabe},
     title = {Regularity results and solution semigroups for retarded functional differential equations},
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     volume = {10},
     number = {1},
     year = {2017},
     language = {en},
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A. Favini; H. Tanabe. Regularity results and solution semigroups for retarded functional differential equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 48-69. http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a3/