We consider the existence of singular limit solution for a nonlinear elliptic system of Liouville type with Navier boundary conditions. We use the nonlinear domain decomposition method. Indeed, we build an exact solution of the problem on small balls centered on singularities and far from those balls so with a suitable choice of data on the edge balls and via a nonlinear Cauchy data matching, the obtained solution is a global one.
Received: September 15, 2019.
Accepted: February 18, 2020.
Published online: April 1st, 2020.
Sami BaraketUniversity of Tunis El Manar, Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia.Abdellatif MessaoudiUniversity of Tunis El Manar, Preparatory Institute for Engineering Studies, El Manar, Tunis 2092 Tunisia.Soumaya SâanouniUniversity of Tunis El Manar, Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia.Nihed TrabelsiUniversity of Tunis El Manar, higher Institut of medicals technologies of Tunis, 9 street Dr. Zouhair Essafi 1006 Tunis, Tunisia.