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We analyze the limit of the solutions of an elliptic problem when some reaction and potential terms are concentrated in a neighborhood of a portion Γ of the boundary and this neighborhood shrinks to Γ as a parameter goes to zero.We prove that this family of solutions converges in certain Sobolev spaces and also in the sup norm, to the solution of an elliptic problem where the reaction term and the concentrating potential are transformed into a flux condition and a potential on Γ.

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In this paper we analyze the long time behavior of a phasefield model by showing the existence of global compact attractors in the strong norm of high order Sobolev spaces.

We obtain nonhomogeneous dynamic boundary conditions as a singular limit of a parabolic problem with null flux and potentials and reaction terms concentrating at the boundary.