Internal null controllability of a linear Schr枚dinger-KdV system on a bounded interval

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• 作者：Fá ; gner D. Araruna^a ; ^{fagner@mat.ufpb.br" class="auth_mail" title="E-mail the corresponding author} ; Eduardo Cerpa^b ; ^{eduardo.cerpa@usm.cl" class="auth_mail" title="E-mail the corresponding author} ; Alberto Mercado^b ; ^{alberto.mercado@usm.cl" class="auth_mail" title="E-mail the corresponding author} ; Maurí ; cio C. Santos^a ; ^c ; ^{mauricio@dmat.ufpe.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dispersive system ; Schrö ; dinger equation ; Korteweg&ndash ; de Vries equation ; Null controllability ; Carleman estimates
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 January 2016
• 年：2016
• 卷：260
• 期：1
• 页码：653-687
• 全文大小：425 K

文摘

The control of a linear dispersive system coupling a Schrödinger and a linear Korteweg–de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrödinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrödinger equation or two real-valued controls, one on each equation. Notice that the single Schrödinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach.