id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-243	Giacomoni, Jacques; Gouasmia, Abdelhamid; Mokrane, Abdelhafid	Existence and global behavior of weak solutions to a doubly nonlinear evolution	2021	37	.pdf	application/pdf	15385	804	82	= ( ‖u‖p Lp(RN ) + ∫ RN ∫ RN |u(x)− u(y)|p |x− y|N+sp dx dy )1/p . • The space W s,p 0 (Ω) is the set of functions W s,p 0 (Ω) := {u ∈W s,p(RN ) : u = 0 a.e. in RN \ Ω}, and the norm is given by the Gagliardo semi-norm ‖u‖W s,p 0 (Ω) := (∫ RN ∫ RN |u(x)− u(y)|p |x− y|N+sp dx dy )1/p . Then, for any r ≥ 1, ‖vq(t, ·)− vq∞‖Lr(Ω) → 0 as t→∞, where v∞ is the unique stationary solution to (1.12) associated to the potential h∞. This article is organized as follows: In Section 2, we study the stationary non- linear problem v2q−1 + λ(−∆)spv = h0(x)vq−1 + λf(x, v) in Ω, v > in Ω, v = 0 in RN \ Ω, related to the parabolic problem (1.12) and establish the existence and the unique- ness results in case h0 ∈ L∞(Ω)	cache/ejde-243.pdf	txt/ejde-243.txt