Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization

Attractors of the Reaction-diffusion Systems with Rapidly Oscillating Coefficients and Their Homogenization Attracteurs Pour Des Systémes De Réaction-diffusion Avec Des Coefficients Oscillant Rapidement Et Leur Homogénéisation

– The following reaction-diffusion system in spatially non-homogeneous almostperiodic media is considered in a bounded domain ⊂R3: ∂tu=Aεu− f (u)+ g, u|∂ = 0. (1) Here u= (u1, . . . , u) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator Aε has the following structure: (Aεu) l = 3 ∑ i,j=1 ∂xi (a l ij (ε −1x)∂xj u(x)), ε 1, l ...

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

Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating terms

Advection-diffusion Problems with Rapidly Oscillating Coefficients and Large Expected Drift. Part 1: Homogenization - Existence, Uniqueness and Regularity

This contribution is concerned with the homogenization of linear advection-diffusion problems with rapidly oscillating coefficient functions and a large expected drift. Even though the homogenization of this type of problems is generally well known, there are several details that have not yet been treated explicitly or even been treated at all. In this paper we will give a survey of this topic ...

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...