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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
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1569-3945
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Volume 22, Issue 2

Issues

An identification problem for a semilinear evolution delay equation

Alfredo Lorenzi
  • Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
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/ Ioan I. Vrabie
  • Faculty of Mathematics, “Al. I. Cuza” University, Iaşi 700506, Romania; and “O. Mayer” Mathematics Institute of the Romanian Academy, Iaşi 700505, Romania
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Published Online: 2013-11-27 | DOI: https://doi.org/10.1515/jip-2013-0020

Abstract.

We prove the existence, uniqueness and continuous dependence on the data of a mild solution to an identification problem for a first-order semilinear delay differential equation in a Banach space subjected to an overdetermination expressed by means of an integral with respect to an absolutely continuous measure (with respect to the Lebesgue measure). Two applications to some identification problems, the first one for a parabolic delay equation and the second one for a hyperbolic delay equation, are also considered.

Keywords: Identification problem; first-order semilinear differential delay equation; unknown source; C0-semigroup of contractions; parabolic equation; first order hyperbolic equation

MSC: 34K29; 34G20; 35K20; 35K90; 35L40; 47D06; 47H10

About the article

Received: 2013-03-20

Published Online: 2013-11-27

Published in Print: 2014-04-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 2, Pages 209–244, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0020.

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