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On the controllability of the BBM equation
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2022-01-25 , DOI: 10.3934/mcrf.2022002
Melek Jellouli

<p style='text-indent:20px;'>In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in <inline-formula><tex-math>\begin{document}$ H^1(\mathbb{T}) $\end{document}</tex-math></inline-formula>. We also show that the equation is not exactly controllable in <inline-formula><tex-math>\begin{document}$ H^s(\mathbb{T}) $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math>\begin{document}$ s\in[1,2[ $\end{document}</tex-math></inline-formula>.</p>

中文翻译:

关于 BBM 方程的可控性

<p style='text-indent:20px;'>在本文中,我们考虑环面上的非线性 BBM 方程。我们使用在有限维空间中取值的控件来证明方程在 <inline-formula><tex-math>\begin{document}$ H^1(\mathbb{T}) $\end{document 中是近似可控的}</tex-math></inline-formula>。我们还证明了方程在 <inline-formula><tex-math>\begin{document}$ H^s(\mathbb{T}) $\end{document}</tex-math>< /inline-formula> 用于 <inline-formula><tex-math>\begin{document}$ s\in[1,2[ $\end{document}</tex-math></inline-formula>。< /p>
更新日期:2022-01-25
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