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Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in R 2

Author

Listed:
  • Jincheng Shi

    (School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China)

  • Yan Liu

    (Department of Mathematics, Guangdong University of Finance, Guangzhou 510521, China)

Abstract

In this paper, we studied the continuous dependence result for the Boussinesq equations. We considered the case where Ω was a bounded domain in R 2 . Temperatures T and C satisfied reaction boundary conditions. A first-order inequality for the differences of energy could be derived. An integration of this inequality produced a continuous dependence result. The result told us that the continuous dependence type stability was also valid for the Boussinesq coefficient λ of the Boussinesq equations with reaction boundary conditions.

Suggested Citation

  • Jincheng Shi & Yan Liu, 2022. "Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in R 2," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:991-:d:774864
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    References listed on IDEAS

    as
    1. Liu, Yan, 2017. "Continuous dependence for a thermal convection model with temperature-dependent solubility," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 18-30.
    2. Evgenii S. Baranovskii, 2021. "Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 623-645, May.
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