Trajectory attractors for reaction-diffusion systems

Trajectory Attractors for Reaction-diffusion Systems

(1) ∂tu = a∆u− f0(u, t) + g0(x, t), u|∂Ω = 0 (or ∂u/∂ν|∂Ω = 0) where u = u(x, t) = (u, . . . , u ), x ∈ Ω b R, t ≥ 0, f0(v, s) = (f 0 , . . . , f 0 ), (v, s) ∈ R × R+, g0(x, s) = (g 0 , . . . , g 0 ), x ∈ Ω, s ≥ 0. We assume that the matrix a and the functions f0, g0 satisfy some general conditions (see Section 2). These conditions provide the existence of a solution u of the Cauchy problem for...

Attractors for Partly Dissipative Reaction Diffusion SYstems in R^n

In this paper, we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in ‫ޒ‬ n. We prove the asymptotic compact-ness of the solutions and then establish the existence of the global attractor in 2 Ž n .

Quantitative Homogenization of Global Attractors For Reaction-Diffusion Systems . . .

Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

Pullback attractors of nonautonomous reaction–diffusion equations

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...