Anguiano, M.; Caraballo, T.; Real, J. \(H^{2}\)-boundedness of the pullback attractor for a non-autonomous reaction-diffusion equation. (English) Zbl 1180.35117 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 876-880 (2010). Summary: We prove some regularity results for the pullback attractor of a reaction-diffusion model. First, we establish a general result about \(H^{2}\)-boundedness of invariant sets for an evolution process. Then, as a consequence, we deduce that the pullback attractor of a non-autonomous reaction-diffusion equation is bounded not only in \(L^2(\varOmega)\cap H_0^1 (\varOmega)\) but also in \(H^{2}(\Omega )\). Cited in 13 Documents MSC: 35B41 Attractors 35Q35 PDEs in connection with fluid mechanics 35K57 Reaction-diffusion equations 35K58 Semilinear parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:invariant sets; \(H^{2}\)-regularity PDFBibTeX XMLCite \textit{M. Anguiano} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 876--880 (2010; Zbl 1180.35117) Full Text: DOI References: [1] Robinson, J. C., Infinite-Dimensional Dynamical Systems (2001), Cambridge University Press · Zbl 1026.37500 [2] Temam, R., Infinite Dimensional Dynamical Systems in Mechanics and Physics (1997), Springer: Springer New York · Zbl 0871.35001 [3] Caraballo, T.; Lukaszewicz, G.; Real, J., Pullback attractors for asymptotically compact non-autonomous dynamical systems, Nonlinear Analysis. Theory Methods & Applications, 64, 484-498 (2006) · Zbl 1128.37019 [4] Caraballo, T.; Lukaszewicz, G.; Real, J., Pullback attractors for non-autonomous 2D Navier-Stokes equations in unbounded domains, Comptes rendus Mathématique, 342, 263-268 (2006) · Zbl 1085.37054 [5] Kloeden, P. E., Pullback attractors of nonautonomous semidynamical systems, Stochastics and Dynamics, 3, 1, 101-112 (2003) · Zbl 1029.37010 [6] Li, Y.; Zhong, C. K., Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations, Applied Mathematics and Computation, 190, 1020-1029 (2007) · Zbl 1126.37049 [7] Song, H.; Wu, H., Pullback attractors of nonautonomous reaction-diffusion equations, Journal of Mathematical Analysis and Applications, 325, 1200-1215 (2007) · Zbl 1104.37013 [8] Song, H.; Zhong, C., Attractors of non-autonomous reaction-diffusion equations in \(L^p\), Nonlinear Analysis, 68, 1890-1897 (2008) · Zbl 1149.35328 [9] Wang, Y.; Zhong, C., On the existence of pullback attractors for non-autonomous reaction-difusion equations, Dynamical Systems, 23, 1, 1-16 (2008) · Zbl 1145.35047 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.