Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion

Article type: Research Article

Authors: Yan, Xingjie^a | Wang, Shubin^b | Yang, Xin-Guang^{c; *} | Zhang, Junzhao^d

Affiliations: [a] Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, P.R. China | [b] School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, P.R. China | [c] Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, P.R. China | [d] Computer Science and Engineering, Changchun University of Technology, Changchun 130012, P.R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L2(Ω) and H0α(Ω) (0<α<1) have been achieved with a restriction on the growth order of nonlinearity as 2⩽p⩽2(n−α)n−2α. The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations.

Keywords: Fractional Laplacian, pullback attractor, non-compactness measure

DOI: 10.3233/ASY-221800

Journal: Asymptotic Analysis, vol. 132, no. 3-4, pp. 495-517, 2023