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Mathematics > Optimization and Control

arXiv:2108.04159 (math)
[Submitted on 9 Aug 2021 (v1), last revised 15 Aug 2021 (this version, v2)]

Title:Boundary controllability for a degenerate and singular wave equation

Authors:Brahim Allal, Alhabib Moumni, Jawad Salhi
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Abstract:In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in the range of subcritical/critical potentials and for sufficiently large time, through a boundary controller acting away from the degenerate/singular point. By duality argument, we reduce the problem to an observability estimate for the corresponding adjoint system, which is proved by means of the multiplier method and a new special Hardy-type inequality.
Comments: 19 pages
Subjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
Cite as: arXiv:2108.04159 [math.OC]
  (or arXiv:2108.04159v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.04159
Related DOI: https://doi.org/10.1002/mma.8464

Submission history

From: Brahim Allal [view email]
[v1] Mon, 9 Aug 2021 16:33:28 UTC (15 KB)
[v2] Sun, 15 Aug 2021 19:17:23 UTC (17 KB)
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