id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2816	Al-Hawasy, jamil Amir; A. Abdul-Hussien Al-Anbaki, Wissam 	The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints	2022	11	.pdf	application/pdf	6471	293	82	= 0 , from the density of {�⃗⃗⃗�𝑘} in �⃗⃗⃗⃗��⃗⃗⃗� , one has 𝐻�⃗⃗⃗�(𝑥, 𝑡, �⃗�, 𝑧 at each �⃗⃗� ∈ �⃗⃗⃗⃗� , ∀𝑙 = 0,1,2 and for every 𝜌 (by hypotheses (A) , (B) and (C) and Lemma 2.1), and 𝐺𝑙(�⃗⃗�) is 𝜌 −differentiable at each �⃗⃗� ∈ �⃗⃗⃗⃗� , ∀𝜌 (by hypotheses (A) , (B) and (C) and The. 3.2) and since �⃗⃗⃗⃗� ⊂ (𝐿2(𝑄)) 4 , 𝐿2(𝑄) is open, then 𝐷𝐺𝑙(�⃗⃗�, �⃗⃗⃗� − �⃗⃗�) = �́�𝑙(�⃗⃗�)(�⃗⃗⃗� − �⃗⃗�) , 𝑙 = 0,1,2, And since �⃗⃗� ∈ �⃗⃗⃗⃗�𝐴 is QCCOCV, by The. 2.4, there is 𝜆𝑙 ∈ ℝ , 𝑙 = 0,1,2 , with 𝜆0 ≥ 0 , 𝜆2 ≥ 0 , ∑ |𝜆𝑙| = 1 2 𝑙=0 s.t. (38a&b) are held.	cache/iajs-2816.pdf	txt/iajs-2816.txt