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.