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Article Contents

# 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.
Mathematics Subject Classification: Primary: 45Q05, 45K05, 45N05, 47D06.

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