id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3650	Ismayilova, Gunay	The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem	2020	9	.pdf	application/pdf	3415	192	75	By a generalized solution of the problem (1), (2) for a given function v(x) ∈ V we mean a function u = u(x, t; v) from U such that for t = 0 it satisfies the condition u(x, 0) = u0(x) and the integral identity∫ Q [ −∂u ∂t ∂η ∂t + n∑ i=1 ∂u ∂xi ∂η ∂xi + vuη ] dxdt− ∫ Ω u1(x)η(x, 0)dx = ∫ Q f(x, t, u)ηdxdt (8) for all η = η(x, t) from U and are equal to zero for t = T . It is clear that, the identities∫ Q [ −∂um ∂t ∂η ∂t + n∑ i=1 ∂um ∂xi ∂η ∂xi + vmumη ] dxdt− − ∫ Ω u1(x)η(x, 0)dx = ∫ Q f(x, t, um)ηdxdt (11) are true for all η ∈ U which are equal to zero at t = T .	cache/ejpam-3650.pdf	txt/ejpam-3650.txt