Exact controllability for a degenerate and singular wave equation with moving boundary | Zendy

Alhabib Moumni | Zendy; Jawad Salhi | Zendy

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Exact controllability for a degenerate and singular wave equation with moving boundary

Author(s) -

Alhabib Moumni,

Jawad Salhi

Publication year - 2022

Publication title -

numerical algebra control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.303

H-Index - 20

eISSN - 2155-3289

pISSN - 2155-3297

DOI - 10.3934/naco.2022001

Subject(s) - controllability , mathematics , degenerate energy levels , mathematical analysis , uniqueness , bounded function , boundary (topology) , wave equation , boundary value problem , hilbert space , physics , quantum mechanics

This paper is concerned with the exact boundary controllability for a degenerate and singular wave equation in a bounded interval with a moving endpoint. By the multiplier method and using an adapted Hardy-poincaré inequality, we prove direct and inverse inequalities for the solutions of the associated adjoint equation. As a consequence, by the Hilbert Uniqueness Method, we deduce the controllability result of the considered system when the control acts on the moving boundary. Furthermore, improved estimates of the speed of the moving endpoint and the controllability time are obtained.

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