Weak convergence of attractors of reaction–diffusion systems with randomly oscillating coefficients. Issue 1 (25th January 2019)

• Record Type: Journal Article
• Authors: Bekmaganbetov, Kuanysh A.; Chechkin, Gregory A.; Chepyzhov, Vladimir V.
• Is Part Of: Applicable analysis. Volume 98:Issue 1/2(2019)
• Page Start: 256
• Page End: 271
• Publication Date: 2019-01-25
• Subjects: Attractors -- random homogenization -- reaction–diffusion systems -- nonlinear equations -- weak convergence; 35B40 -- 35B41 -- 35B45 -- 35Q30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1400538
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider reaction–diffusion systems with random rapidly oscillating coefficient. We do not assume any Lipschitz condition for the nonlinear function in the system, so, the uniqueness theorem for the corresponding initial-value problem may not hold for the considered reaction–diffusion system. Under the assumption that the random function is ergodic and statistically homogeneous in space variables we prove that the trajectory attractors of these systems tend in a weak sense to the trajectory attractors of the homogenized reaction–diffusion systems whose coefficient is the average of the corresponding term of the original systems.