Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles

Abstract

We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems in the strong topology of the corresponding trajectory dynamical systems. By means of generalized Fatou’s lemma we prove the strong convergence of the trajectory attractors of considered systems to the trajectory attractors of the corresponding homogenized reaction–diffusion systems which contain an additional potential.

Keywords

• trajectory attractors
• homogenization
• reaction–diffusion systems
• non-linear equations
• strong convergence