Abstract:
In this paper the Ginzburg-Landau equation is considered in locally periodic porous medium, with rapidly
oscillating terms in the equation and boundary conditions. It is proved that the trajectory attractors of
this equation converge in a weak sense to the trajectory attractors of the limit Ginzburg-Landau equation
with an additional potential term. For this aim we use an approach from the papers and monographs of
V.V. Chepyzhov and M.I. Vishik concerning trajectory attractors of evolution equations. Also we apply
homogenization methods appeared at the end of the XX-th century. First, we apply the asymptotic methods
for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means
of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional
spaces with weak topology, we derive the limit (homogenized) equation and prove the existence of trajectory
attractors for this equation. Then we formulate the main theorem and prove it with the help of axillary
lemmas.
