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<p>This paper studies the controllability properties of a class of higher-order unidirectional dispersive equations on a finite domain. Focusing on a linearized model with boundary control inputs, we show that exact controllability fails due to spectral properties. Nevertheless, we establish approximate controllability by employing spectral analysis techniques. These results generalize existing work on both lower- and higher-order Boussinesq-type systems and contribute to the theory of boundary control for higher-order wave equations.</p>

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On the lack of controllability of a higher-order water wave model

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • George J. Bautista,
  • Oscar A. Sierra Fonseca

摘要

This paper studies the controllability properties of a class of higher-order unidirectional dispersive equations on a finite domain. Focusing on a linearized model with boundary control inputs, we show that exact controllability fails due to spectral properties. Nevertheless, we establish approximate controllability by employing spectral analysis techniques. These results generalize existing work on both lower- and higher-order Boussinesq-type systems and contribute to the theory of boundary control for higher-order wave equations.