Remarks on semilinear parabolic systems with terms concentrating in the boundary

We are concerned with the asymptotic behavior of a dynamical system generated by a family of semilinear parabolic systems with reaction and potential terms concentrating in a neighborhood of a portion of the boundary. Assuming that this neighborhood shrinks to this section as a parameter ϵϵ goes to zero, we exhibit the limit problem and show continuity of the flux as well as upper and lower semicontinuity of the family of global attractors with respect to ϵϵ using an appropriated functional setting on suitable conditions for the system. It is worth noting that oscillatory behavior to the neighborhood as ϵϵ goes to zero is also allowed providing a large range of applications.