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<p>In this article, we establish Carleman estimates for degenerate wave operators, focusing on cases where degeneracy occurs only on a portion of the boundary. Under specific geometrical assumptions, we construct novel weight functions tailored to address the challenges posed by the degeneracy, thereby deducing global Carleman estimates. As applications, we prove the exact controllability (both boundary and internal) for the degenerate wave equation using the Hilbert Uniqueness Method.</p>

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Carleman Estimates and Controllability for Degenerate Wave Equations

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Guang Zhang,
  • Shugen Chai

摘要

In this article, we establish Carleman estimates for degenerate wave operators, focusing on cases where degeneracy occurs only on a portion of the boundary. Under specific geometrical assumptions, we construct novel weight functions tailored to address the challenges posed by the degeneracy, thereby deducing global Carleman estimates. As applications, we prove the exact controllability (both boundary and internal) for the degenerate wave equation using the Hilbert Uniqueness Method.