Attractors for reaction–diffusion equations on thin domains whose linear part is non-self-adjoint

For a bounded smooth domain (omega)(subset) R(Nx+Ny) let (omega)(epsilon), 0<(epsilon), be a family of domains squeezed in y (element of) R(Ny) direction. On (omega)(epsilon) we consider a reaction–diffusion equation with nonsymmetrical linear part. We show that under natural conditions on the nonlinearity the generated semi-flows have global attractors which in a certain sense have limits, as (epsilon) (down arrow)0.