Attractors for the Nonlinear Elliptic Boundary Value Problems and Their Parabolic Singular Limit
نویسنده
چکیده
We apply the dynamical approach to the study of the second order semilinear elliptic boundary value problem in a cylindrical domain with a small parameter ε at the second derivative with respect to the variable t corresponding to the axis of the cylinder. We prove that, under natural assumptions on the nonlinear interaction function f and the external forces g(t), this problem possesses the uniform attractor Aε and that these attractors tend as ε → 0 to the attractor A0 of the limit parabolic equation. Moreover, in case where the limit attractor A0 is regular, we give the detailed description of the structure of the uniform attractor Aε, if ε > 0 is small enough, and estimate the symmetric distance between the attractors Aε and A0.
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