Flux condition induced by concentrated reactions

Abstract

We analyze the limit of solutions of an elliptic problem, with zero flux boundary conditions when the reaction terms are concentrated in a neighborhood of the boundary and that shrinks to the boundary as a parameter goes to zero. We prove that this family of solutions converges, in the sup norm, to the solution of an elliptic problem with no reaction terms and with a nonhomogeneous flux condition. This non zero flux condition for the limiting problem comes from the concentrated reactions around the boundary of the domain.