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arXiv · 2402.06301

On the control of the Burgers-alpha model

Fágner D. Araruna·Enrique Fernández-Cara·Diego A. Souza
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Abstract

This work is devoted to prove the local null controllability of the Burgers-$\alpha$ model. The state is the solution to a regularized Burgers equation, where the transport term is of the form $zy_x$, $z=(Id-\alpha^2\frac{\partial^2}{\partial x^2})^{-1}y$ and $\alpha>0$ is a small parameter. We also prove some results concerning the behavior of the null controls and associated states as $\alpha\to 0^+$.

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Fágner D. Araruna, Enrique Fernández-Cara, Diego A. Souza. 2024-02-09. On the control of the Burgers-alpha model. https://doi.org/10.57262/ade/1372777764

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