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

✍ Scribed by M. Efendiev; S. Zelik

• Book ID: 104324262
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 217 KB
• Volume: 19
• Category: Article
• ISSN: 0294-1449
• DOI: 10.1016/s0294-1449(02)00115-4

✦ Synopsis

The following reaction-diffusion system in spatially non-homogeneous almostperiodic media is considered in a bounded domain ⊂ R 3 :

(1)

Here u = (u 1 , . . . , u k ) is an unknown vector-valued function, f is a given nonlinear interaction function and the second order elliptic operator A ε has the following structure:

where a l ij (y) are given almost-periodic functions. We prove that, under natural assumptions on the nonlinear term f (u), the longtime behavior of solutions of (1) can be described in terms of the global attractor A ε of the associated dynamical system and that the attractors A ε , 0 < ε < ε 0 1, converge to the attractor A 0 of the homogenized problem (1) as ε → 0. Moreover, in the