OPTIMAL-CONTROL AND REGULARIZATION TO MODEL THE ATMOSPHERIC ELECTRON-CONTENT FROM SATELLITE MEASUREMENTS

We are conceived with the completing of the electron content of the io nosphere. There already exists a statistical model, the model of Bent [1], which has been derived from physical delta. The accuracy of this model appears to be insufficient when we deal with the real data that we get from satellite measurements. Our aim is to derive a mathematica l model from the equations of the physical model. The problem is ill-p osed since it has an infinity of solutions. It is penalized and regula rized by laking into account the values predicted by the model of Bent . Hence, the problem is tuned into an optimal control problem, the sta te of which is the electron content. This problem is discretized in sp aces of splines and error estimates are derived. We give the numerical results we have computed from the data of the satellite SPOT-2. (C) E lsevier, Paris.