id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1119	Nie, Yuanyuan; Leng, Yan; Zhao, Xu; Zhou, Qian	Critical Fujita exponents for a class of quasilinear coupled parabolic  equations	2025	18	.pdf	application/pdf	6314	329	82	Introduction In this article, we study the critical Fujita exponent for the Cauchy problem of quasilinear coupled parabolic equations ∂u ∂t = ∆um + (|x|+ 1)λvp, x ∈ Rn, t > 0, (1.1) ∂v ∂t = ∆vm + (|x|+ 1)µuq, x ∈ Rn, t > 0, (1.2) u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Rn, (1.3) where p, q > m > 1, λ ≥ 0, µ = λ(q −m) + 2(q − p) p−m ≥ 0 (1.4) and 0 ≤ u0, v0 ∈ C0(Rn) are nontrivial. It was demonstrated that the Cauchy problem of the heat equation ∂u ∂t = ∆u+ up, x ∈ Rn, t > 0 admits no nontrivial nonnegative global solution when 1 < p < pc = 1 + 2/n, otherwise, it admits both nontrivial global (with small initial data) and nonglobal nonnegative (with large initial data) solutions when p > pc.	cache/ejde-1119.pdf	txt/ejde-1119.txt