id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5017	Mebarki, Maroua	Asymptotic Behavior of Global Solution of an Anomalous Gray Scott Model	2024	14	.pdf	application/pdf	4394	272	83	For λ ∈ [0, 1] and µ ∈ R, there exists a constant M (λ, µ) such that, for all t ≻ 0, ∫ t 0 c(s)−λeµsds ≤  M (λ, µ) eµt, if µ ≻ 0, M (λ, µ) (t+ 1), if µ = 0, M (λ, µ) , if µ ≺ 0, here c(t) = min{t, 1}. [0, T ] :{ w(t) = e−d1tSpw0 + ∫ t 0 e −d1(t−s)Sp(−w2z + f(1− w))ds, z(t) = e−d2tTpz0 + ∫ t 0 e −d2(t−s)Tp(w2z − (f + k)z)ds. (11) Theorem 1. local existence Let w0, z0 ∈ C ( Ω ) , then there exist a maximal time Tmax ≻ 0 and a unique mild solution (w, z) ∈C ( [0, Tmax);C ( Ω ) × C ( Ω )) to the system (1)-(2) , with the alternative: -either Tmax = +∞; -or	cache/ejpam-5017.pdf	txt/ejpam-5017.txt