Regularity and identification for an integrodifferentialone-dimensional hyperbolic  equation

Alfredo Lorenzi; Eugenio Sinestrari

doi:10.3934/ipi.2009.3.505

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2009, Volume 3, Issue 3: 505-536. Doi: 10.3934/ipi.2009.3.505

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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: August 2009

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Abstract

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.

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

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