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Sidewise control of 1-d waves

Submission Status:under review
  • We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path at the otherfree end. This sidewise control problem is also often referred to as nodal profile or tracking control. First, the problem is reformulated as a dual observability property for the corresponding adjoint system. Using sidewiseenergy propagation arguments the sidewise observability is shown to hold, ina sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.

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Author:Yesim Sarac, Enrique Zuazua
Document Type:Article
Language:English
Date of Publication (online):2021/01/05
Date of first Publication:2021/01/07
Release Date:2021/01/07
Tag:1-d wave equations; BV-coefficients; nodal profile con-trol
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International