id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-520	Kurima, Shunsuke	Time discretization of an abstract problem from linearized equations of a coupled sound and heat flow	2020	26	.pdf	application/pdf	9497	415	86	h2(Φλϕλ, ϕλ)H = (g, ϕλ)H − h2(Lϕλ − L0, ϕλ)H − h2(L0, ϕλ)H − ηh2(B2(I + hA1)−1ϕλ, ϕλ)H ≤ cL 2 ‖ϕλ‖2H + 1 2cL ‖g‖2H + CLh 2‖ϕλ‖2H + ‖L0‖2H 2 h2 + 1 2 h2‖ϕλ‖2H + ηCA1,B2 (h+ h2)‖ϕλ‖2H , whence the conditions (A2) and (A3), the monotonicity of B1 and Φλ imply that there exists h1 ∈ (0,min{1, h̃}) such that for all h ∈ (0, h1) there exists a constant C2 = C2(h) > 0 satisfying ‖ϕλ‖2V ≤ C2 (3.3) for all λ > 0. (4.17) Condition (A6) and Lemma 4.1 mean that there exists a constant C1 = C1(T ) > 0 such that − h (Φϕn+1 − Φϕn h , zn+1 ) H ≤ CΦh(1 + ‖ϕn+1‖pV + ‖ϕn‖qV )‖vn+1‖V ‖zn+1‖H ≤ C1h‖vn+1‖V ‖zn+1‖H (4.18) for all h ∈ (0, h2).	cache/ejde-520.pdf	txt/ejde-520.txt