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<p>We study the local null controllability of the viscous Burgers equation on the whole line. The control is assumed to be distributed along an equidistributed set <i>ω</i>. We first prove a uniform upper bound on costs of local null controls for the viscous Burgers equation on a sequence {Ω<sub><i>n</i></sub>}<sub><i>n</i>⩾1</sub> of increasing domains, where the controls are acted on Ω<sub><i>n</i></sub> ∩ <i>ω.</i> Then letting <i>n</i> tend to infinity and making use of the smoothing effect of the viscous Burgers equation, we obtain the main result.</p>

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Local null controllability of the viscous Burgers equation on the whole line

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Lijuan Wang,
  • Anlei Zhang,
  • Can Zhang

摘要

We study the local null controllability of the viscous Burgers equation on the whole line. The control is assumed to be distributed along an equidistributed set ω. We first prove a uniform upper bound on costs of local null controls for the viscous Burgers equation on a sequence {Ωn}n⩾1 of increasing domains, where the controls are acted on Ωn ∩ ω. Then letting n tend to infinity and making use of the smoothing effect of the viscous Burgers equation, we obtain the main result.