Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in <i>R</i>²

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 R2. 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