id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-548	Yan, Jianlu; Li, Yuxiang	Existence and boundedness of solutions for a Keller-Segel system with gradient dependent chemotactic sensitivity	2020	14	.pdf	application/pdf	5571	319	84	Finally, for arbitrary non-negative ψ ∈ C∞0 (Ω̄× [0,∞)), multiplying the second equation in (2.7) by ψ, and integrating by parts, we have∫ Ω v0ψ(·, 0) + ∫ T 0 ∫ Ω vεψt = ∫ T 0 ∫ Ω ∇vε · ∇ψ + ∫ T 0 ∫ Ω vεψ − ∫ T 0 ∫ Ω uεψ (3.19) for all ε ∈ (0, 1). − χ∇ · ( u∇v√ 1 + |∇v|2 ) , 0 = ∆v −M + u, (1.5) where M = 1 |Ω| ∫ Ω u0(x)dx, n ≥ 2 and χ < 1.	cache/ejde-548.pdf	txt/ejde-548.txt