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<p>In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, non-local differential operator inherent in the dynamics of a two-dimensional, incompressible, non-viscous fluid within a confined domain. Our work establishes unique continuation results that enable the application of source control localized in an interior domain, allowing the aforementioned controllability.</p>

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On the unique continuation property for the two-dimensional sloshing problem

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月4日

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  • M. Fontelos,
  • R. Lecaros,
  • J. López-Ríos,
  • A. A. Pérez

摘要

In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, non-local differential operator inherent in the dynamics of a two-dimensional, incompressible, non-viscous fluid within a confined domain. Our work establishes unique continuation results that enable the application of source control localized in an interior domain, allowing the aforementioned controllability.