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<p>This paper deals with controllability properties of a cubic Ginzburg–Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the domain. In order to achieve this result, we first linearize the system around the origin and analyze it by the duality approach and an appropriate Carleman estimate. Then, using an inverse function theorem, the local null controllability of the nonlinear system is proven.</p>

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Local null controllability of a cubic Ginzburg–Landau equation with dynamic boundary conditions

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Nicolás Carreño,
  • Alberto Mercado,
  • Roberto Morales

摘要

This paper deals with controllability properties of a cubic Ginzburg–Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the domain. In order to achieve this result, we first linearize the system around the origin and analyze it by the duality approach and an appropriate Carleman estimate. Then, using an inverse function theorem, the local null controllability of the nonlinear system is proven.