id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2833	Al-Hawasy, jamil Amir; Abd Alsatar Hassan, Mayeada 	The Optimal Classical Continuous Control Quaternary Vector of Quaternary Nonlinear Hyperbolic Boundary Value Problem	2022	14	.pdf	application/pdf	8392	289	80	�⃗⃗�𝑘 → �⃗⃗� WK in (𝐿2(𝑄))4 and ∥ �⃗⃗�𝑘 ∥𝑄≤ 𝑑,∀𝑘. From Theorem 3.1, for each control {�⃗⃗�𝑘} the WF (18), (20), (22), (24) has a unique SQVS , {�⃗�𝑘 = �⃗�𝑢𝑘 } s.t. By using Lemma (1.2), to acquire ∥ �⃗� − �⃗̅� ∥0 2≤ 0𝑒 ∫ 0 𝑇 2𝐿𝑑𝑡 = 0, ∀𝑡 ∈ 𝐼 Again IBS of (68) w.r.t. 𝑡 from 0 to 𝑇, using the ICs and the above result for the RHS of the equations, to acquire ∫ 0 𝑇 𝑑 𝑑𝑡 ∥ �⃗� − �⃗̅� ∥0 2+ 2 ∥ �⃗� − �⃗̅� ∥1 2 𝑑𝑡 ≤ 𝐿 ∫ 0 𝑇 ∥ (�⃗� − �⃗̅�) ∥0 2 𝑑𝑡 ⟹ ∫ 0 𝑇 ∥ (�⃗� − �⃗̅�) (𝑡) ∥1 2≤ 0 ⟹∥ (�⃗� − �⃗̅�) (𝑡) ∥𝐿2(I,V)	cache/iajs-2833.pdf	txt/iajs-2833.txt