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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Representation formulae for solutions to direct and inverse degenerate in time first-order Cauchy problems in Banach spaces

A. Lorenzi1

1Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 5, Pages 477–497, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.030, July 2009

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We are concerned with a degenerate in time first-order identification problem related to a closed operator in a Banach space. The degeneracy with respect to time — due to scalar time coefficients — is assumed to be integrable. For both direct and inverse problem we exhibit explicit representations of the solutions in terms of the linear operator A and function ƒ (cf. equation (1.1)), when the latter possess specific properties.

Some applications to partial differential equations are given.

Key words.: Degenerate in time differential equations in Banach spaces; Representation formulae for direct and inverse problems; Application to parabolic PDE's

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