  We apply the dynamical approach to the study of the second order semi-linear
elliptic boundary value problem in a cylindrical domain with a small parameter
at the second derivative with respect to the "time" variable corresponding to
the axis of the cylinder.
  We prove that, under natural assumptions on the nonlinear interaction
function and the external forces, this problem possesses the uniform attractors
and that these attractors tend to the attractor of the limit parabolic
equation. Moreover, in case where the limit attractor is regular, we give the
detailed description of the structure of these uniform attractors when the
perturbation parameter is small enough, and estimate the symmetric distance
between the perturbed and non-perturbed attractors.
