Abstract: When the internal nonlinearity and boundary nonlinearity adhered to polynomial growth of arbitrary order as well as the balance condition, and the forcing term was only translation bounded rather than translation compact, we considered the asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary condition and weak fading memory. By using the contractive function method and the new prior estimate technique, we proved the existence and gave topology structure of uniform attractors on topological space L²(Ω)×L²_μ(R⁺;L²(Ω)).

Key words: non-autonomous classical reaction-diffusion equation, nonlinear boundary, weak fading memory, polynomial growth of arbitrary order