Uniform attractors for nonautonomous reaction-diffusion equations with the nonlinearity in a larger symbol space

Existence and structure of the uniform attractors for reaction-diffusion equations with the nonlinearity in a weaker topology space are considered. Firstly, a weaker symbol space is defined and an example is given as well, showing that the compactness can be easier obtained in this space. Then the existence of solutions with new symbols is presented. Finally, the existence and structure of the uniform attractor are obtained by proving the \begin{document}$ (L^{2}\times \Sigma, L^{2}) $\end{document} -continuity of the processes generated by solutions.