Regularity Results and Solution Semigroups for Retarded Functional Differential Equations

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.

References

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