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arXiv · 2101.00473

Sidewise control of 1-d waves

Yesim Sarac·Enrique Zuazua
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Abstract

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 other free 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 sidewise energy propagation arguments the sidewise observability is shown to hold, in a 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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Yesim Sarac, Enrique Zuazua. 2021-01-02. Sidewise control of 1-d waves. https://arxiv.org/abs/2101.00473

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