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arXiv · 2108.04159

Boundary controllability for a degenerate and singular wave equation

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.

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Brahim Allal, Alhabib Moumni, Jawad Salhi. 2021-08-09. Boundary controllability for a degenerate and singular wave equation. https://doi.org/10.1002/mma.8464

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