id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3069	Azizbayov, Elvin Ibrahim; Mehraliyev, Yashar	Inverse Problem for a Parabolic Equation with Integral Condition	2017	14	.pdf	application/pdf	4295	234	81	Problem Statement Denote by QT the domain {(x, t) : 0 ≤ x ≤ 1, 0 ≤ t ≤ T} and consider the equation c(t)ut(x, t) = uxx(x, t) + a(t)u(x, t) + b(t)g(x, t) + f(x, t), (x, t) ∈ QT (1) with nonlocal initial condition u(x, 0) + δu(x, T ) = ϕ(x) (0 ≤ x ≤ 1), (2) Neumann boundary condition ux(0, t) = 0 (0 ≤ t ≤ T ), (3) nonlocal integral condition 1∫ 0 u(x, t)dx = 0 (0 ≤ t ≤ T ), (4) and the additional conditions u(0, t) = h1(t) (0 ≤ t ≤ T ), (5) u(1, t) = h2(t) (0 ≤ t ≤ T ), (6) where δ ≥ 0 is a fixed number, 0 < c(t), g(x, t), f(x, t), 0 ≤ p(t), hi(t) (i = 1, 2) are given functions, u(x, t), a(t) and b(t) are unknown functions. [13] T.E. Oussaeif and A. Bouziani, Inverse problem of a hyperbolic equation with an integral overdetermination condition, Electronic Journal of Differential Equations, 2016(138):1-7, 2016.	cache/ejpam-3069.pdf	txt/ejpam-3069.txt