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arXiv · 2204.03427

Stabilisation of a viscous conservation law by a one-dimensional external force

Ana Djurdjevac·Armen Shirikyan
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Abstract

We study a damped scalar conservation law driven by the sum of a fixed external force and a localised one-dimensional control. The problem is considered in a bounded domain and is supplemented with the Dirichlet boundary condition. It is proved that any solution of the uncontrolled equation can be exponentially stabilised. As a consequence, we obtain the global approximate controllability to trajectories by a one-dimensional localised control.

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Ana Djurdjevac, Armen Shirikyan. 2022-04-07. Stabilisation of a viscous conservation law by a one-dimensional external force. https://arxiv.org/abs/2204.03427

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