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ON BOUNDARY EXACT CONTROLLABILITY OF ONE-DIMENSIONAL WAVE EQUATIONS WITH WEAK AND STRONG INTERIOR DEGENERATION
  • Günter Leugering,
  • Peter Kogut,
  • Olga Kupenko
Günter Leugering
University Erlangen-Nuremberg
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Peter Kogut
Dnipropetrovsk National University
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Olga Kupenko
National Technical University ”Dnipro Polytechnics”
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Abstract

In this paper we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficients in the principle part of the elliptic operator. The objective is to provide a well-posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

Peer review status:ACCEPTED

26 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
04 Jul 2020Submission Checks Completed
04 Jul 2020Assigned to Editor
10 Aug 2020Reviewer(s) Assigned
14 Oct 2020Review(s) Completed, Editorial Evaluation Pending
14 Oct 2020Editorial Decision: Revise Major
12 Nov 20201st Revision Received
12 Nov 2020Submission Checks Completed
12 Nov 2020Assigned to Editor
13 Nov 2020Reviewer(s) Assigned
03 Jan 2021Review(s) Completed, Editorial Evaluation Pending
04 Jan 2021Editorial Decision: Revise Major
16 Jan 20212nd Revision Received
16 Jan 2021Submission Checks Completed
16 Jan 2021Assigned to Editor
18 Jan 2021Reviewer(s) Assigned
10 Jun 2021Review(s) Completed, Editorial Evaluation Pending
08 Jul 2021Editorial Decision: Revise Minor
14 Jul 20213rd Revision Received
14 Jul 2021Assigned to Editor
14 Jul 2021Submission Checks Completed
14 Jul 2021Reviewer(s) Assigned
10 Aug 2021Review(s) Completed, Editorial Evaluation Pending
10 Aug 2021Editorial Decision: Accept