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- W3116366976 abstract "<p style='text-indent:20px;'>We examine the asymptotic behavior of the non-autonomous non-local fractional stochastic reaction-diffusion equations on <inline-formula><tex-math id=M2>begin{document}$ mathbb{R}^{N} $end{document}</tex-math></inline-formula> with the nonlinearity <inline-formula><tex-math id=M3>begin{document}$ f $end{document}</tex-math></inline-formula> satisfying the polynomial growth of arbitrary order <inline-formula><tex-math id=M4>begin{document}$ p-1 $end{document}</tex-math></inline-formula> <inline-formula><tex-math id=M5>begin{document}$ (pgeq2) $end{document}</tex-math></inline-formula>. We first establish a Nash-Moser-Alikakos type a priori estimate for the difference of solutions near the initial time. Then, we prove that the solution process is continuous from <inline-formula><tex-math id=M6>begin{document}$ L^{2}(mathbb{R}^{N}) $end{document}</tex-math></inline-formula> to <inline-formula><tex-math id=M7>begin{document}$ H^{s}(mathbb{R}^{N}) $end{document}</tex-math></inline-formula> with respect to initial data for <inline-formula><tex-math id=M8>begin{document}$ sin(0, 1) $end{document}</tex-math></inline-formula>. As an application of the higher-order integrability and the continuity, we obtain the pullback <inline-formula><tex-math id=M9>begin{document}$ mathcal{D} $end{document}</tex-math></inline-formula>-random attractors in <inline-formula><tex-math id=M10>begin{document}$ L^{p}(mathbb{R}^{N}) $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M11>begin{document}$ H^{s}(mathbb{R}^{N}) $end{document}</tex-math></inline-formula>, respectively. This is a natural and necessary extension of current existing results to further understand the dynamics of the underlying problem." @default.
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- W3116366976 date "2021-01-01" @default.
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- W3116366976 title "Dynamics of non-autonomous fractional reaction-diffusion equations on $ mathbb{R}^{N} $ driven by multiplicative noise" @default.
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- W3116366976 doi "https://doi.org/10.3934/dcdsb.2020376" @default.
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