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.