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

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Abstract

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.

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Funding

This work was supported by the Science and Technology Research Project of the Education Department of Jilin Province (No. JJKH20210031KJ), the Science and Technology Development Project of Jilin Province (No. 20230101001JC), and the National Natural Science Foundation of China (No. 12001227).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beihua University, Jilin, 132013, People’s Republic of China

    Wei Guo

  2. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Mingjun Zhou & Ningning Man

  3. Changchun No. 8 High School, Changchun, 130012, People’s Republic of China

    Ningning Man

Authors
  1. Wei Guo
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  2. Mingjun Zhou
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  3. Ningning Man
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Correspondence to Mingjun Zhou.

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Guo, W., Zhou, M. & Man, N. Carleman estimate and null controllability for a degenerate convection–diffusion equation. Comp. Appl. Math. 44, 187 (2025). https://doi.org/10.1007/s40314-025-03165-3

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  • DOI: https://doi.org/10.1007/s40314-025-03165-3

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