Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 91, pp. 1-19.
Title: Strong solutions for some nonlinear partial functional
differential equations with infinite delay
Authors: Mohamed Alia (Univ. Cadi Ayyad, Morocco)
Khalil Ezzinbi (Univ. Cadi Ayyad, Morocco)
Abstract:
In this work, we use the Kato approximation to prove the
existence of strong solutions for partial functional differential
equations with infinite delay. We assume that the undelayed part
is $m$-accretive in Banach space and the delayed part is Lipschitz
continuous. The phase space is axiomatically defined. Firstly, we
show the existence of the mild solution in the sense of Evans.
Secondly, when the Banach space has the Radon-Nikodym property, we
prove the existence of strong solutions. Some applications are
given for parabolic and hyperbolic equations with delay. The
results of this work are extensions of the Kato-approximation
results of Kartsatos and Parrot [8,9].
Submitted October 25, 2007. Published June 21, 2008.
Math Subject Classifications: 34K30, 37L05, 47H06, 47H20.
Key Words: Partial functional differential equations;
infinite delay; m-accretive operator; Kato approximation;
mild solution in the sense of Evans; strong solution;
Radon-Nikodym property.