Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 31, pp. 1-14.

Title: Existence and analyticity of a parabolic evolution operator
       for nonautonomous linear equations in Banach spaces
   
Authors: Antonio S. Munhoz (Univ. Federal do Espirito Santo, Brazil)
         Antonio C. Souza Filho (Univ. de Sao Paulo, Brazil)

Abstract:
 We give conditions for the parabolic evolution operator
 to be analytic with respect to a coefficient operator.
 We also show that the solution of a homogeneous parabolic evolution
 equation is analytic with respect to the coefficient operator and
 to the initial data.  We apply our results to example that
 can not be studied by the standard methods.
 
Submitted July 20, 2007. Published February 09, 2009.
Math Subject Classifications: 35K90, 46T25, 47N20, 47L05.
Key Words: Linear equation; parabolic equation; nonautonomous.