"Strange term" in homogenization of attractors of reaction–diffusion equation in perforated domain. (November 2020)

• Record Type: Journal Article
• Authors: Bekmaganbetov, Kuanysh A.; Chechkin, Gregory A.; Chepyzhov, Vladimir V.
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Attractors -- Homogenization -- Reaction-diffusion -- Equation -- Nonlinear equations -- Weak convergence -- Perforated domain -- Strange term; 35B40 -- 35B41 -- 35Q80; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110208
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Reaction-diffusion equation in perforated domain with rapidly oscillating coefficient Trajectory attractors tend to the trajectory attractors of the homogenized equation Weak convergence and effective behavior of attractors "Strange term" (the potential in the limit equation) Abstract: We consider reaction–diffusion equation in perforated domain, with rapidly oscillating coefficient in boundary conditions. We do not assume any Lipschitz condition for the nonlinear function in the equation, so, the uniqueness theorem for the corresponding initial boundary value problem may not hold for the considered reaction-diffusion equation. We prove that the trajectory attractors of this equation tend in a weak sense to the trajectory attractors of the homogenized reaction-diffusion equation with a "strange term" (potential). Bibliography: 48 titles.