Advances in Differential Equations

On the control of the Burgers-alpha model

Fágner D.. Araruna, Enrique Fernández-Cara, and Diego A. Souza

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This work is devoted to proving 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 $\alpha\to 0^+$.

Article information

Adv. Differential Equations, Volume 18, Number 9/10 (2013), 935-954.

First available in Project Euclid: 2 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93B05: Controllability 35Q35: PDEs in connection with fluid mechanics 35G25: Initial value problems for nonlinear higher-order equations


Araruna, Fágner D.; Fernández-Cara, Enrique; Souza, Diego A. On the control of the Burgers-alpha model. Adv. Differential Equations 18 (2013), no. 9/10, 935--954.

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