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CONTROL OF KAWAHARA EQUATION WITH OVERDETERMINATION CONDITION: THE UNBOUNDED CASES
  • Roberto Capistrano Filho,
  • S. LUAN Soares de Sousa,
  • A. FERNANDO GALLEGO
Roberto Capistrano Filho
Universidade Federal de Pernambuco

Corresponding Author:[email protected]

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S. LUAN Soares de Sousa
Universidade Federal de Pernambuco
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A. FERNANDO GALLEGO
Universidad Nacional de Colombia Sede Manizales
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Abstract

Abstract. In this manuscript we consider the internal control problem for the fifth order KdV type equation, commonly called the Kawahara equation, on unbounded domains. Precisely, under certain hypotheses over the initial and boundary data, we are able to prove that there exists an internal control input such that solutions of the Kawahara equation satisfies an integral overdetermination condition. This condition is satisfied when the domain of the Kawahara equation is posed in the real line, left half-line and right half-line. Moreover, we are also able to prove that there exists a minimal time in which the integral overdetermination condition is satisfied. Finally, we show a type of exact controllability associated with the “mass” of the Kawahara equation posed in the half-line.
09 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
10 Mar 2022Submission Checks Completed
10 Mar 2022Assigned to Editor
30 Nov 2022Reviewer(s) Assigned
03 Mar 2023Review(s) Completed, Editorial Evaluation Pending
06 Mar 2023Editorial Decision: Revise Minor
06 Mar 20231st Revision Received
07 Mar 2023Submission Checks Completed
07 Mar 2023Assigned to Editor
07 Mar 2023Review(s) Completed, Editorial Evaluation Pending
18 Mar 2023Reviewer(s) Assigned
25 Apr 2023Editorial Decision: Accept