id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1353	Li, Xingquan; Feng, Yuli; Yan, Han	Global existence and blow-up for the viscoelastic damped wave equation on the Heisenberg group	2025	12	.pdf	application/pdf	5392	294	83	= ∫ R 0 ∫ T 0 ∫ Hn |u(t, η)|p(Φ∗ r) 3p′ r−1 dη dt dr, combining the estimates (5.5) with (5.6), we have 2J(R) log 2 + ϵI(u0, u1) ≲ R −2+Q+1 p′ (RJ ′(R))1/p, EJDE-2025/71 GLOBAL EXISTENCE AND BLOW-UP 11 which gives R 2p− p(Q+1) p′ −1 ≲ J ′(R) (2J(R) log 2 + ϵI(u0, u1) )−p , (5.7) where I(u0, u1) For all T > 0, we define the operator N for u ∈ X(T ) as Nu = ulin + unlin = ϵu0 ∗(η) E0(t, η) + ϵu1 ∗(η) E1(t, η) + ∫ t 0 |u|p ∗(η) E1(t− s, η)ds Theorem 1.1 will be proved by showing that ∥Nu∥X(T )	cache/ejde-1353.pdf	txt/ejde-1353.txt