STABILITY ANALYSIS FOR A CONTAMINANT CONVECTION-REACTION-DIFFUSION MODEL OF RECOVERED FRACTURING FLUID

The aim of this paper is to study the stability analysis for a contaminant convection-reactiondiffusion model of the recovered fracturing fluid (RFFM, for short), which couples a nonlinear and nonsmooth stationary incompressible Navier-Stokes equation with a multivalued frictional boundary condition, and a nonlinear reaction-diffusion equation with mixed Neumann boundary conditions. First, we introduce a family of perturbation problems corresponding to (RFFM), and present the variational formulation of perturbation problem which is a perturbation elliptic hemivariational inequality driven by a perturbation nonlinear variational equation. Then, the existence of solutions and the uniform bound of the solution set to the perturbation problem are obtained. Finally, it is established that, as the perturbation parameter tends to zero, the solution set of the perturbation problems converge to the solution set of (RFFM) in the sense of the Kuratowski upper limit. This shows that (RFFM) is stable with respect to the perturbation data.