id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6488	Begaidarov, Muminbek ; Bibulova, Dana; Kalimbetov, Burkhan	Asymptotic Solutions to a Singularly Perturbed Partial Integro-Differential Equation with a Rapidly Oscillating Right-Hand Side	2025	20	.pdf	application/pdf	7398	432	73	Math, 18 (4) (2025), 6488 13 of 20 ≤ c0k0 x∫ x0 ||w(ζ, ε)||dζ + c0k1 x∫ x0 ζ∫ x0 ||w(s, ε)||dsdζ+ + X0 ε c0||Φ(x, ε)||C[x0,X]×[0,T ] ≤ c0k0 x∫ x0 ||w(s, ε)||ds+ +c0k1 x∫ x0 x∫ x0 ||w(s, ε)||dsdζ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] ≤ ≤ c0k0 x∫ x0 ||w(s, ε)||ds+ c0k1 X∫ x0 x∫ x0 ||w(s, ε)||dsdζ+ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] ≤ (c0k0 + c0k1X0) x∫ x0 ||w(s, ε)||ds+ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] where X0 = X − x0, ||K(x, t, s)||C[x0,X]×[0,T ] = k0, ||∂K(x,t,s) ∂x ||C[x0,X]×[0,T ] = k1. ∂u ∂τj − λ1(x)u− x∫ x0 K(x, t, s)u(s, t, ψ(s)ε , ε)ds = h1(x, t)+ +h2(x, t)e τ2σ, u(x0, t, 0, ε) = y0(t), ( (x, t) ∈	cache/ejpam-6488.pdf	txt/ejpam-6488.txt