Open AccessUniform attractors for nonautonomous reaction-diffusion equations with the nonlinearity in a larger symbol space
Author(s) -
Zhu Xiangming,
Chen Zhong
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021212
Subject(s) - attractor , space (punctuation) , compact space , mathematics , symbol (formal) , reaction–diffusion system , nonlinear system , diffusion , pure mathematics , mathematical analysis , physics , computer science , quantum mechanics , programming language , operating system
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.