id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-329	Messaoudi, Salim A.; Bouhoufani, Oulia; Hamchi, Ilhem; Alahyane, Mohamed	Existence and blow up in a system of wave equations with nonstandard nonlinearities	2021	33	.pdf	application/pdf	11145	590	86	, ωk}, as follows uk(x, t) = Σkj=1aj(t)ωj(x), vk(t) = Σkj=1bj(t)ωj(x), for x ∈ Ω and t ∈ (0, T ), satisfying the approximate problems∫ Ω uktt(x, t)ωjdx+ ∫ Ω A∇uk(x, t) · ∇ωjdx + ∫ Ω |ukt (x, t)|m(x)−2ukt (x, t)ωjdx = ∫ Ω f(x, t)ωjdx,∫ Ω vktt(x, t)ωjdx+ ∫ Ω B∇vk(x, t) · ∇ωjdx + ∫ Ω |vkt (x, t)|r(x)−2vkt (x, t)ωjdx = ∫ Ω g(x, t)ωjdx, (3.5) for j Introduction In this work, we study the following initial-boundary-value problem for the un- knowns u and v: utt − div(A∇u) + |ut|m(x)−2ut = f1(x, u, v) in Ω× (0, T ), vtt − div(B∇v) + |vt|r(x)−2vt = f2(x, u, v) in Ω× (0, T ), u = v = 0 on ∂Ω× (0, T ), u(0) = u0, ut(0) = u1 in Ω, v(0)	cache/ejde-329.pdf	txt/ejde-329.txt