On the Asymptotics of Attractors of the Ginzburg–Landau Complex Equation in a Perforated Domain with an Oscillating Boundary: Subcritical Case

We study the asymptotic behavior of trajectory attractors for the Ginzburg–Landau complex equation in a perforated domain with a rapidly oscillating outer boundary when the parameter characterizing the pore sizes and the distance between them, as well as the amplitude and frequency of the boundary oscillation, tends to zero. In the subcritical case (the Fourier boundary condition is changed to the Neumann boundary condition in the limit), we prove that the trajectory attractors of this system converge in a weak sense to the trajectory attractors of the limit (homogenized) Ginzburg–Landau complex systems of equations in a domain independent of the small parameter, characterizing the oscillation rate. Then, we formulate the main theorem and prove it with the help of auxiliary lemmas.