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Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping
  • Boumediène Chentouf
Boumediène Chentouf
Kuwait University
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Abstract

The aim of this article is to investigate the well-posedness and stability problems of the so-called Kawahara equation under the presence of an interior delayed damping. The system is shown to be well-posed. Furthermore, we prove that the trivial solution is exponentially stable in spite of the delay effect. Specifically, local and semi-global stability results are established according to the properties of the spatial distribution of the delay term.
02 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
03 Jan 2022Submission Checks Completed
03 Jan 2022Assigned to Editor
17 Jan 2022Reviewer(s) Assigned
19 Apr 2022Review(s) Completed, Editorial Evaluation Pending
20 Apr 2022Editorial Decision: Revise Minor
23 Apr 20221st Revision Received
25 Apr 2022Submission Checks Completed
25 Apr 2022Assigned to Editor
25 Apr 2022Reviewer(s) Assigned
28 Apr 2022Review(s) Completed, Editorial Evaluation Pending
28 Apr 2022Editorial Decision: Accept