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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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Peer review status:UNDER REVIEW

26 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
04 Jul 2020Assigned to Editor
04 Jul 2020Submission Checks Completed
10 Aug 2020Reviewer(s) Assigned

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.