id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-2759	Alaa, Noureddine; Aqel, Fatima	Global Existence of Solutions for a System Modelling Electromigration of Ions Through Biological Cell Membranes with L1 Data	2017	23	.pdf	application/pdf	8141	402	80	Math, 10 (2) (2017), 272-294 279 which means that by passing to the limit, we obtain∫ T 0 ∫ Ω ∂(qi,nZi,n) ∂t sign−(Zi,n) ≤ 0 therefore ∫ T 0 ∫ Ω ∂(qi,nZi,n)− ∂t ≤ 0 this implies the following inequality∫ Ω (qi,nZi,n)−(t, x) ≤ ∫ Ω (qi,nZi,n)−(0, x) as (qi,nZi,n)(0, x) ≥ 0 for almost everywhere then we deduce∫ Ω (qi,nZi,n)−(t, x) ≤ 0. Using now the boundary conditions to obtain∫ QT ∂t(jk(qi,nZi,n)) + di ∫ QT ∇Tk(qi,nZi,n)(qi,n∇Zi,n) = ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) which implies that∫ QT ∂t(jk(qi,nZi,n)) + di ∫ QT T ′ k(qi,nZi,n)|qi,n∇Zi,n|2 = ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) +mi ∫ QT T ′ k(qi,nZi,n)(qi,n∇Zi,n)(qi,nZi,n)∇φn the integration over (0, T ) yields to the equality above∫ Ω jk(qi,nZi,n)(t) + di ∫ QT T ′ k(qi,nZi,n)|qi,n∇Zi,n|2 = ∫ Ω jk(q n i,0Z n i,0) + ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) + mi ∫ QT T ′ k(qi,nZi,n)(qi,n∇Zi,n)(qi,nZi,n)∇φn.	cache/ejpam-2759.pdf	txt/ejpam-2759.txt