Startseite Identification of an unknown coefficient in KdV equation from final time measurement
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Identification of an unknown coefficient in KdV equation from final time measurement

  • Kumarasamy Sakthivel EMAIL logo , Soundararajan Gnanavel , Alemdar Hasanov und Raju K. George
Veröffentlicht/Copyright: 27. Mai 2016

Abstract

In this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg–de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the unknown coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the coefficient is also discussed.

MSC 2010: 35Q53; 45Q05; 49J20

Funding statement: The first author is supported by the Department of Science and Technology, Government of India through INSPIRE research grant.

The authors are thankful to the suggestions of reviewers which helped to improve the manuscript.

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Received: 2016-2-4
Revised: 2016-4-6
Accepted: 2016-4-22
Published Online: 2016-5-27
Published in Print: 2016-8-1

© 2016 by De Gruyter

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