Asymptotic behavior of interior transition layers for nonlinear boundary-value problem with small parameter

Abstract

The system of equations $$(D(|E|)(n' + nE))' = 0, E' = f - n, 0< x< 1,$$ with the boundary conditions $$E(0) = a_0 , E(1) = \alpha _1 , D(|E(0)|)(n'(0) + n(0)E(0)) = j_0 $$ is considered. The solvability of this boundary-value problem and properties of the family of solutions are studied under the condition that the diffusion coefficient is negative. Bibliography: 5 titles.