On singular perturbation problems for the nonlinear Poisson equation

Article type: Research Article

Authors: Ambroso, A. | Méhats, F. | Raviart, P.A.

Affiliations: CMAP (UMR 7641), École Polytechnique, F‐91128 Palaiseau, France | MIP (UMR 5640)–UFR MIG, Université Paul Sabatier, 118 route de Narbonne, F‐31062 Toulouse, France

Abstract: We study a singular perturbation problem for the nonlinear Poisson equation and we classify its solutions. This classification is based on their monotonicity properties, which mainly depend on the stationary points of the so‐called Sagdeev potential. For each class of solution, we give necessary and sufficient conditions for the resolution of the problem and provide a boundary layer analysis.

Keywords: nonlinear Poisson equation, singular perturbation problem, Sagdeev potential, boundary layer

Journal: Asymptotic Analysis, vol. 25, no. 1, pp. 39-91, 2001