Regularity and identification for an integrodifferential one-dimensional hyperbolic equation

In this paper we determine a (possibly) non-continuous scalar relaxation kernel of bounded variation in an integrodifferential equation related to a Banach space when a nonlocal additional measurement involving the state function is available. We prove a result concerning global existence and uniqueness. An application is given, in the framework of space of continuous functions, to the case of one-dimensional hyperbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions.