On the control of the Burgers-alpha model

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 $z{y}_x$, $z=(Id-{\alpha }^2\frac{{\partial }^2}{\partial x^2}{)}^{-1}y$ and $\alpha >0$ is a small parameter. We also prove some results concerning the behavior of the null controls and associated states as $\alpha \to 0^{+}$.

22 pages

Cited by in corpus (1)

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