caa a22 4500 378896490 CHVBK 20180305123507.0 cr unu---uuuuu 161128e20041001xx s 000 0 eng 10.1515/1569394042248238 doi (NATIONALLICENCE)gruyter-10.1515/1569394042248238 Reconstruction of boundary data for a class of nonlinear inverse problems [Elektronische Daten] [M. Essaouini, A. Nachaoui, S. El Hajji] In this paper we present a new formulation for the nonlinear Cauchy problem for elliptic equations. This formulation allows us to give a method for solving this class of problems. The nonlinear problem is reduced to a linear Cauchy problem for the Laplace equation coupled with a sequence of nonlinear scalar equations. We solve the linear problem using the iterative method introduced in [7]. The linear dense systems obtained from a boundary element approximation are solved using an efficient implementation which accelerate the iterative process. Various types of convergence, comparison results and effects of small perturbations on boundary data are investigated. The numerical results show that the method produces a stable good approximate solution. Copyright 2004, Walter de Gruyter Essaouini M. Département de Mathématiques & Informatique, Faculté des sciences, Université Med V, B.P. 1014, Rabat, Maroc. E-mail: elhajji@fsr.ac.ma aut Nachaoui A. CNRS, UMR 6629, Université de Nantes, B.P. 92208, F-44322 Nantes, France. E-mail: nachaoui@math.univ-nantes.fr aut Hajji S. El Département de Mathématiques & Informatique, Faculté des sciences, Université Med V, B.P. 1014, Rabat, Maroc. E-mail: elhajji@fsr.ac.ma aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/4(2004-10-01), 369-385 0928-0219 12:4<369 2004 12 jiip https://doi.org/10.1515/1569394042248238 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569394042248238 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Essaouini M. Département de Mathématiques & Informatique, Faculté des sciences, Université Med V, B.P. 1014, Rabat, Maroc. E-mail: elhajji@fsr.ac.ma aut NATIONALLICENCE 700 1- Nachaoui A. CNRS, UMR 6629, Université de Nantes, B.P. 92208, F-44322 Nantes, France. E-mail: nachaoui@math.univ-nantes.fr aut NATIONALLICENCE 700 1- Hajji S. El Département de Mathématiques & Informatique, Faculté des sciences, Université Med V, B.P. 1014, Rabat, Maroc. E-mail: elhajji@fsr.ac.ma aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/4(2004-10-01), 369-385 0928-0219 12:4<369 2004 12 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter