ftp ejde.math.txstate.edu EXISTENCE AND ANALYTICITY OF A PARABOLIC EVOLUTION OPERATOR FOR NONAUTONOMOUS LINEAR EQUATIONS IN BANACH SPACES

Abstract. We give conditions for the parabolic evolution operator to be an-alytic 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. 1