On Attractors of Reaction-Diffusion Equations in a Porous Orthotropic Medium

A system of reaction-diffusion equations in a perforated domain with rapidly oscillating terms in the equation and in the boundary conditions is studied. A nonlinear function in the equations may not satisfy the Lipschitz condition and, hence, the uniqueness theorem for the corresponding initial-boundary value problem for the considered system of reaction-diffusion equations may not be satisfied. It is proved that the trajectory attractors of this system weakly converge in the corresponding topology to the trajectory attractors of the homogenized reaction-diffusion system with a strange term (potential).

Automated summary

The system of reaction-diffusion equations in a perforated domain with rapidly oscillating terms was studied, showing weak convergence of trajectory attractors to a homogeneous system with a strange term in the corresponding topology.