id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-83	Shen, Xuhui; Ding, Juntang	Blow-up for parabolic equations in nonlinear divergence form with time-ependent coefficients	2022	17	.pdf	application/pdf	6277	287	86	xj − k(t)f(u) in Ω × (0, t∗), n∑ i,j=1 aij(x)uxiνj = g(u) on ∂Ω × (0, t∗), u(x, 0) = u0(x) ≥ 0 in Ω, where Ω is a bounded convex domain in Rn (n ≥ 2) with smooth boundary ∂Ω. By constructing suitable auxiliary functions and using a differential inequality technique, when Ω ⊂ Rn (n ≥ 2) Published January 25, 2022. 1 2 X. SHEN, J. DING EJDE-2022/08 ( h(u) ) t = n∑ i,j=1 ( aij(x)uxi ) xj − k(t)f(u) in Ω× (0, t∗), n∑ i,j=1 aij(x)uxi νj = g(u) on ∂Ω× (0, t∗), u(x, 0) = u0(x) ≥ 0 in Ω, (1.1) where Ω is a bounded convex domain in Rn (n ≥ 2) with smooth boundary ∂Ω, (aij(x))n×n is a differentiable positive definite matrix, ν is the outward normal vector to ∂Ω, u0(x) is the initial value, t∗ is the maximal existence time of u, and Ω is the closure of Ω. Set R+ = (0,+∞).	cache/ejde-83.pdf	txt/ejde-83.txt