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Journal of Optimization Theory and Applications

, Volume 180, Issue 1, pp 290–302 | Cite as

Control Problems with an Integral Condition for Korteweg–de Vries Equation on Unbounded Domains

  • Andrei V. FaminskiiEmail author
Article
  • 71 Downloads

Abstract

The initial and initial-boundary value problems, posed on infinite domains for Korteweg–de Vries equation, are considered. The right-hand side of the equation contains an unknown function, regarded as a control, which must be chosen such that the corresponding solution should satisfy certain additional integral condition. Results on existence and uniqueness are established in the cases of small input data or small time interval.

Keywords

Control Initial-boundary value problem Integral condition Korteweg–de Vries equation 

Mathematics Subject Classification

49N45 35Q53 35Q93 

Notes

Acknowledgements

The publication was prepared with the support of the “RUDN University Program 5-100”, Ministry of Education and Science of the Russian Federation (Project 1.962.2017/PCh) and RFBR Grants 17-01-00849, 17-51-52022, 18-01-00590.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Peoples’ Friendship University of Russia (RUDN University)MoscowRussian Federation

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