id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6073	Al-Mahdi, Adel M. ; Al-Gharabli, Mohammad; M. D. Kassim; Abdelaziz Soufyane; Mostafa Zahri; Mukiawa, Soh Edwin 	Controllability of a System with Nonlinear Damping Devices and Nonlinear Source Terms in Elasticity Problems: Existence, Time Blow-up, and Numerical Results	2025	29	.pdf	application/pdf	9774	541	78	As k goes to +∞, we easily check that ∀j < k, ∫ Ω ztwj(x)dx− ∫ Ω z1wj(x)dx+ a1 ∫ t 0 ∫ Ω zxwjx(x)dxds+ a2 ∫ t 0 ∫ Ω uxwjx(x)dxds + γ ∫ t 0 ∫ Ω |zt|p(.)−2ztwj(x)dxds = ∫ t 0 ∫ Ω wjf(x, t)dxds,∫ Ω utwj(x)dx− ∫ Ω u1wj(x)dx+ a3 ∫ t 0 ∫ Ω uxwjx(x)dxds+ a2 ∫ t 0 ∫ Ω zxwjx(x)dx + β ∫ t 0 ∫ Ω |ut|q(.)−2utwj(x)dxds = ∫ t 0 ∫ Ω wjg(x, t)dxds. Messaoudi [27]considered the following nonlinear viscoelastic wave equation utt −∆u+ ∫ t 0 g(t− s)∆u(s)ds+ a|ut|m−2ut = b|u|p−2u, x ∈ Ω, t > 0, (8) where Ω is a bounded domain of Rn.	cache/ejpam-6073.pdf	txt/ejpam-6073.txt