id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-510	Bouhoufani, Oulia; Messaoudi, Salim A.; Zahri, Mostafa	Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents	2023	20	.pdf	application/pdf	7360	391	80	A pair of functions (u, v) is said to be a weak solution of (1.1) on [0, T ), if u, v ∈ L∞((0, T ), H1 0 (Ω)), ut, vt ∈ L∞((0, T ), L2(Ω)), ut ∈ Lm(·) α (Ω× (0, T )), vt ∈ Lr(·)β (Ω× (0, T )) and (u, v) satisfies∫ Ω utφdx− ∫ Ω u1φdx+ ∫ t 0 ∫ Ω α(τ)|ut|m(x)−2utφdx dτ + ∫ t 0 ∫ Ω ∇u.∇φdx dτ + ∫ t 0 ∫ Ω |u|p(x)−2u|v|p(x)φdx dτ = 0 and ∫ Ω vtψ dx− ∫ Ω v1ψ dx+ ∫ t 0 ∫ Ω β(τ)|vt|r(x)−2vtψ dx dτ + ∫ t 0 ∫ Ω ∇v.∇ψ dx dτ + ∫ t 0 ∫ Ω |v|p(x)−2v|u|p(x)ψ dx dτ = 0, for all φ, ψ ∈ H1 0 (Ω) and all t ∈ (0, T ), with (u(·, 0), v(·, 0)) = {w : Ω× (0, T )→ R : ∫ T 0 ∫ Ω β(τ)|w(x, τ)|r(x) dx dτ < +∞}.	cache/ejde-510.pdf	txt/ejde-510.txt