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

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  • In this paper we prove both the existence and uniqueness of a solution to an identification problem for a first order linear differential equation in a general Banach space. Namely, we extend the explicit representation for the solution of this problem previously obtained by Anikonov and Lorenzi [1] to the case of an infinitesimal generator of an analytic $C_0$-semigroup of contractions to the general nonanalytic case and also to the case of a restriction expressed in terms of an operator-valued measure. So, our abstract result handles both parabolic and hyperbolic equations and systems.
    Mathematics Subject Classification: Primary: 35R30, 35K20, 35K90, 34G10.


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  • [1]

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