# American Institute of Mathematical Sciences

August  2009, 3(3): 505-536. doi: 10.3934/ipi.2009.3.505

## Regularity and identification for an integrodifferential one-dimensional hyperbolic equation

 1 Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano 2 Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma

Received  October 2008 Revised  May 2009 Published  July 2009

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.
Citation: Alfredo Lorenzi, Eugenio Sinestrari. Regularity and identification for an integrodifferential one-dimensional hyperbolic equation. Inverse Problems & Imaging, 2009, 3 (3) : 505-536. doi: 10.3934/ipi.2009.3.505
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