Volume 10, no. 1Pages 48 - 69 # Regularity Results and Solution Semigroups for Retarded Functional Differential Equations

A. Favini, H. TanabeWe 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.

Full text- Keywords
- retarded functional differential equation; regularity of solutions; analytic semigroup; solution semigroup; C_0-semigroup; infinitesimal generator.
- References
- 1. Di Blasio G., Lorenzi A. Identification Problems for Integro-Differential Delay Equations. Differential Integral Equations, 2003, vol. 16, no. 11, pp. 1385-1408.

2. Favini A., Tanabe H. Identification Problems for Integrodifferential Equations with Delay: an Improvement of the Results from G. Di Blasio and A. Lorenzi. Appear in Funkcialaj Ekvacioj.

3. Di Blasio G., Kunisch K., Sinestrari E. L^2-regularity for Parabolic Partial Integrodifferential Equations with Delay in the Highest-Order Derivatives. Journal of Mathematical Analysis and Applications, 1984, vol. 102, issue 1, pp. 38-57. DOI: 10.1016/0022-247X(84)90200-2

4. Sinestrari E. On a Class of Retarded Partial Differential Equations. Mathematische Zeitschrift, 1984, vol. 186, pp. 223-246.

5. Di Blasio G. Linear Parabolic Evolution Equations in L^p-Spaces. Annali di Matematica Pura ed Applicata (IV), 1984, vol. 138, issue 1, pp. 55-104. DOI: 10.1007/BF01762539

6. Seeley R. Interpolation in L^p with Boundary Conditions. Studia Matematica, 1972, vol. 44, pp. 47-60.

7. Triebel H. Interpolation Theory, Function Spaces, Differential Operators. Amsterdam, N.Y., Oxford, North-Holland, 1978.