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

Jincheng Shi and Yan Liu
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Jincheng Shi: School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China
Yan Liu: Department of Mathematics, Guangdong University of Finance, Guangzhou 510521, China

Mathematics, 2022, vol. 10, issue 6, 1-14

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.

Keywords: structural stability; Boussinesq equations; Darcy equations; reaction boundary condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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