An identification problem for a linear evolution equation in a Banach space and applications

Abstract

In this paper we prove both the existence anduniqueness of a solution to an identification problem for a firstorder linear differential equation in a general Banach space.Namely, we extend the explicit representation for the solution ofthis problem previously obtained by Anikonov andLorenzi [1] to the case of an infinitesimal generator ofan analytic $C_0$-semigroup of contractions to the generalnonanalytic case and also to the case of a restriction expressed interms of an operator-valued measure. So, our abstract result handlesboth parabolic and hyperbolic equations and systems.