STABILITY IN THE INITIAL-TIME GEOMETRY PROBLEM FOR THE BRINKMAN AND DARCY EQUATIONS OF FLOW IN POROUS-MEDIA

The initial-time geometry problem, where not all of the data assigned at t = 0 are measured at precisely the same instant of time, is invest igated for the equations of flow in porous media known as the Darcy an d Brinkman equations. A sufficient a priori condition on the data is d erived such that the error which may arise in the solution to the forw ard in time problem for the Darcy equations is controllable. A similar a priori error bound is obtained for a solution to the Brinkman equat ions forward in time. The improperly posed backward in time problem is also studied for both the Brinkman and Darcy equations. A stability e stimate is obtained for this case provided the solutions are suitably constrained.