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We apply the dynamical approach to the study of the second order semi-linearelliptic boundary value problem in a cylindrical domain with a small parameterat the second derivative with respect to the "time" variable corresponding tothe axis of the cylinder.  We prove that, under natural assumptions on the nonlinear interactionfunction and the external forces, this problem possesses the uniform attractorsand that these attractors tend to the attractor of the limit parabolicequation. Moreover, in case where the limit attractor is regular, we give thedetailed description of the structure of these uniform attractors when theperturbation parameter is small enough, and estimate the symmetric distancebetween the perturbed and non-perturbed attractors.

Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit