id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3577	Ampini, Dieudonne; Vital Delmas, Mabonzo	Existence of Optimal Control for a Nonlinear Partial Differential Equation of Hyperbolic Type	2019	7	.pdf	application/pdf	2100	104	79	Main operators We shall consider the following problem ∂2u ∂t2 −∆u+ |u|ρu = f(x, t), ρ > 0, (1) ∂u ∂~n (x, t)|∂Ω = 0, t ∈ (0, T ) = ∫ QT K(x, t, x′, t′, [A(f, ϕ, ψ)](x′, t′)dx′dt′ where • the function K : Q̄2 T × R −→ R, K : (x, t, x′, ξ) −→ K(x, t, x′, t′, ξ) is continuous on Q̄2 T × R, differentiable with respect to ξ on R for all (x, t, x′, t′) ∈ Q̄2 T ; • the derived function K ′ξ :	cache/ejpam-3577.pdf	txt/ejpam-3577.txt