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<p>This paper investigates the null controllability of a control system governed by a convection–diffusion equation with weak degeneracy on the boundary. In this governing equation, the convection term cannot be controlled by the diffusion term. We derive a Carleman estimate for the adjoint system through an appropriate transformation that effectively combines the convection and diffusion terms into a complex union, accompanied by detailed computations. Consequently, we establish the observability inequality, and then the control system is proved to be null controllable.</p>

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Carleman estimate and null controllability for a degenerate convection–diffusion equation

  • 期刊论文

  • 发表日期：

    2025年3月15日

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  • Wei Guo,
  • Mingjun Zhou,
  • Ningning Man

摘要

This paper investigates the null controllability of a control system governed by a convection–diffusion equation with weak degeneracy on the boundary. In this governing equation, the convection term cannot be controlled by the diffusion term. We derive a Carleman estimate for the adjoint system through an appropriate transformation that effectively combines the convection and diffusion terms into a complex union, accompanied by detailed computations. Consequently, we establish the observability inequality, and then the control system is proved to be null controllable.