id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1110	Son, Dang Thanh	Long-time behavior of solutions to the 2D magnetic B\'enard problem in porous media on unbounded domains	2025	30	.pdf	application/pdf	12225	628	81	In the next Lemma, we show that the map Λ(t; z0) is bounded and the semigroup {S(t)}t≥0 is uniformly differentiable on global attractor A, i.e., lim ε→0 sup 0<|z̄0−z0|<ε, z̄0,z0∈A |S(t)z̄0 − S(t)z0 − Λ(t; z0)(z̄0 − z0)| |z̄0 − z0| = 0. (5.2) Then for r = 1, 3, there exists a constantM(|z̄0|, |z0|) such that |S(t)z̄0 − S(t)z0 − Λ(t; z0)(z̄0 − z0)| ≤M |z̄0 − z0|, (5.3) where the linear operator Λ(t; z0) for t > 0 is the solution operator of the prob- lem (5.1).	cache/ejde-1110.pdf	txt/ejde-1110.txt