id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-897	Huang, Rui; Ji, Shanming; Ma, Yansheng	Cauchy problem for the Lane-Emden heat flow with sign-changing initial data	2024	13	.pdf	application/pdf	5350	231	75	Comparison principle of the heat equation implies that u(x, t) ≥ u(x) for t ∈ (0, Tmax), which means that Ω̂+ u0 ⊂ Ω+ u(x,t) and Ω− u(x,t) ⊂ v(x)dx ≥ (1− α1−p) (∫ Ω̂+ u0 u+(x, t) · v(x)dx )p(∫ Ω̂+ u0 v(x)dx )1−p = (1− α1−p) · (∫ Ω̂+ u0 v(x)dx )1−p zp(t), t ∈ (τ, Tmax), (2.10) which implies that z(t) blows up in finite time since p > 1 and z(τ) > 0. □ Proof of Theorem 1.1.	cache/ejde-897.pdf	txt/ejde-897.txt