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Observability Inequality from Measurable Sets for Degenerate Parabolic Equations and its Applications

Author

Listed:
  • Yuanhang Liu

    (Central South University)

  • Weijia Wu

    (Central South University)

  • Donghui Yang

    (Central South University)

  • Can Zhang

    (Wuhan University)

Abstract

In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the degenerate parabolic equation over measurable subsets in the time-space domain. As a direct application, we formulate a captivating Stackelberg–Nash game problem and provide a proof of the existence of its equilibrium. Additionally, we characterize the set of Stackelberg–Nash equilibria and delve into the analysis of a norm optimal control problem.

Suggested Citation

  • Yuanhang Liu & Weijia Wu & Donghui Yang & Can Zhang, 2024. "Observability Inequality from Measurable Sets for Degenerate Parabolic Equations and its Applications," Journal of Optimization Theory and Applications, Springer, vol. 200(3), pages 1017-1055, March.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:3:d:10.1007_s10957-023-02359-1
    DOI: 10.1007/s10957-023-02359-1
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