id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-955	Ma, Wenhui; Ma, Qiaozhen	Random attractors and their stability for nonclassical diffusion equations driven by additive white noise with delay and intensity	2025	16	.pdf	application/pdf	8303	385	77	Then for every τ ∈ R, ω ∈ Ω, ϵ ∈ (0, 1] and D = {D(τ, ω) : τ ∈ R, ω ∈ Ω} ∈ D, the solution of problem (3.4)-(3.5) satisfies ∥ d dt v(t, τ − t, θ−τω, ψ)∥2H1(Rn) ≤ Q1(∥v(t, τ − t, θ−τω, ψ)∥2H1(Rn) + ∥g(t)∥2 + ϵ|y(θt−τω)|2 + ∥u(t− ρ, τ − t, θ−τω, ϕ)∥2H1(Rn) + 1), (4.14) where Q1 > 0 is a constant independent of τ, ω,D and ψ ∈ D(τ − t, θ−tω). Proof. Then for every τ ∈ R, ω ∈ Ω, s ∈ [−ρ, 0], D = {D(τ, ω) : τ ∈ R, ω ∈ Ω} ∈ D and ψ ∈ D(τ − t, θ−tω), the solution of problem (3.4)-(3.5) satisfies lim k,t→+∞ ∫ Oc k ∥v(τ + s, τ − t, θ−τω, ψ)∥2H1(Rn)dx = 0. (4.22) Proof.	cache/ejde-955.pdf	txt/ejde-955.txt