Convergence and continuous dependence for the Brinkman-Forchheimer equations

The Brinkman-Forchheimer equations for non-slow flow in a saturated porous medium are analyzed. It is shown that the solution depends continuously on changes in the Forchheimer coefficient, and convergence of the solution of the Brinkman-Forchheimer equations to that of the Brinkman equations is ded uced, as the Forchheimer coefficient tends to zero. The next result establi shes continuous dependence on changes in the Brinkman coefficient. Followin g this, a result is proved establishing convergence of a solution of the Br inkman-Forchheimer equations to a solution Of the Darcy-Forchheimer equatio ns, as the Brinkman coefficient (effective viscosity) tends to zero. Finall y, upper and lower bounds are derived for the energy decay rate which estab lish that the energy decays exponentially, but not faster than this.