Differentiability of the Solutions of a Semilinear Abstract Cauchy Problems With Respect to Parameters

Abstract

The Frechet di®erentiability with respect to a parameter q of the solutions z(t; q) of Cauchy problems of the form d/dt z(t) = A(q)z(t) + F(q; t; z(t)) is analyzed. Su±cient conditions on the operator A(q) and on F are derived and the corresponding sensitivity equations for the Frechet derivative Dqz(t; q) are found.