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- W1995190939 abstract "In this paper, we introduce a new class of functions satisfying spacial absolutely continuous (see Definition 3.1), denoted by documentclass[12pt]{minimal}begin{document}$L^{2}_{sac}(mathbb {R};mathbb {R}^{n})$end{document}Lsac2(R;Rn), which are translation bounded but not normal (see [S. S. Lu, H. Q. Wu, and C. K. Zhong, “Attractors for non-autonomous 2D Navier-Stokes equations with normal external forces,” Discrete Contin. Dyn. Syst. A 13(3), 701−719 (2005)]10.3934/dcds.2005.13.701 and Definition 3.1) in documentclass[12pt]{minimal}begin{document}$L^{2}_{loc}(mathbb {R};mathbb {R}^{n})$end{document}Lloc2(R;Rn). Then the asymptotic a priori estimate is applied to some nonlinear reaction-diffusion equations with external forces documentclass[12pt]{minimal}begin{document}$g(x,s)in L^{2}_{sac}(mathbb {R};mathbb {R}^{n})$end{document}g(x,s)∈Lsac2(R;Rn). We obtain the existence of uniform attractor together with its structure in the bi-spaces documentclass[12pt]{minimal}begin{document}$(L^{2}(mathbb {R}^{n}), L^{2}(mathbb {R}^{n}))$end{document}(L2(Rn),L2(Rn)) and documentclass[12pt]{minimal}begin{document}$(L^{2}(mathbb {R}^{n}), L^{p}(mathbb {R}^{n}))(p>2)$end{document}(L2(Rn),Lp(Rn))(p>2) without any restriction on the growing order of the nonlinear term." @default.
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- W1995190939 date "2012-08-01" @default.
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- W1995190939 title "The existence of uniform attractors for non-autonomous reaction-diffusion equations on the whole space" @default.
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- W1995190939 doi "https://doi.org/10.1063/1.4746693" @default.
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