Abstract:
In the present paper, reaction–diffusion systems (RD-systems) with rapidly oscillating
coefficients and righthand sides in equations and in boundary conditions were considered in domains
with locally periodic oscillating (wavering) boundary. We proved a weak convergence of the trajectory
attractors of the given systems to the trajectory attractors of the limit (homogenized) RD-systems in
domain independent of the small parameter, characterizing the oscillation rate. We consider the critical
case in which the type of boundary condition was preserved. For this aim, we used the approach of
Chepyzhov and Vishik concerning trajectory attractors of evolutionary equations. Also, we applied the
homogenization (averaging) method and asymptotic analysis to derive the limit (averaged) system and
to prove the convergence. Defining the appropriate axillary functional spaces with weak topology, we
proved the existence of trajectory attractors for these systems. Then, we formulated the main theorem
and proved it with the help of auxiliary lemmata.
