id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4135	Ramazanova, Aysel	Necessary Conditions for the Existence of a Saddle Point in one Optimal Control Problem for Systems of Hyperbolic Equations	2021	13	.pdf	application/pdf	4684	197	79	Then it is clear that the increment ∆z (t, x) state, (zo (t, x) , yo (t, x)) satisfies the conditions ∆zt x (t, x) = f (t, x, z̄ (t, x) , z̄t (t, x) , z̄x (t, x) , ū (t, x) , v̄ (t, x))− −f (t, x, zo (t, x) , zot (t, x) , zox (t, x) , uo (t, x) , vo (t, x)) , (t, x) ∈ D , (6) ∆z (t0, x) = ∆a (x) , x ∈ [x0, x1] ∆z (t, x0) = = t1∫ t0 x1∫ x0 [(H (t, x, z (t, x) , zt (t, x) , zx (t, x) , u (t, x) , v (t, x) , ψ o (t, x))− −H (t, x, zo (t, x) , zot (t, x) , z o x (t, x) , u (t, x) , v (t, x) , ψ o (t, x)))+ + (H (t, x, zo (t, x) , zot (t, x) , z o x (t, x) , u (t, x) , v (t, x) , ψ o (t, x))− −H (t, x, zo (t, x) , zot (t, x) , z o x (t, x) , u o (t, x) , vo (t, x) , ψo (t, x)))] .	cache/ejpam-4135.pdf	txt/ejpam-4135.txt