id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-594	Li, Yuequn; Liu, Hui; Guo, Fei	Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion	2024	31	.pdf	application/pdf	10909	623	89	(4.9) Substituting (4.7) into (3.3) gives fs − y 2 fy − 1 2 f = g, s > 0, y ∈ R, e−s b2(t(s)) (gs − 3 2 g − y 2 gy) + g = (a(yes/2)fy)y + α(s)(a0(yes/2)ϕ′0(y))y + h(s, y), s > 0, y ∈ R, f(0, y) = v(0, y)− α(0)ϕ0(y), y ∈ R, g(0, y) = w(0, y)− α̇(0)ϕ0(y)− α(0)ψ0(y), y ∈ R, (4.10) where h(s, y) = e−s b2(t(s)) ( −2α̇(s)ψ0(y) + α(s)( y 2 ψ′0(y) + 3 2 ψ0(y)) ) + r(s, y)− ϕ0(y) ∫ R r(s, y)dy, (4.11) here we have used (4.5) and a(x) = ã(x) + a0(x).	cache/ejde-594.pdf	txt/ejde-594.txt