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

Regularity and identification for an integrodifferential one-dimensional hyperbolic equation

Alfredo Lorenzi 1, and  Eugenio Sinestrari 2,

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.
Keywords: Hille-Yosida semigroups, existence and uniqueness results, Recovering an unknown kernel, linear second-order integro-differential equations in Banach spaces, application to linear hyperbolic integro-differential equations in one dimension..
Mathematics Subject Classification: Primary: 45Q05, 45K05, 45N05, 47D0.
Citation: Alfredo Lorenzi, Eugenio Sinestrari. Regularity and identification for an integrodifferential one-dimensional hyperbolic equation. Inverse Problems and Imaging, 2009, 3 (3) : 505-536. doi: 10.3934/ipi.2009.3.505
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