Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles
We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/6/1448 |
| _version_ | 1827748818879250432 |
|---|---|
| author | Kuanysh A. Bekmaganbetov Gregory A. Chechkin Vladimir V. Chepyzhov |
| author_facet | Kuanysh A. Bekmaganbetov Gregory A. Chechkin Vladimir V. Chepyzhov |
| author_sort | Kuanysh A. Bekmaganbetov |
| collection | DOAJ |
| description | We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems in the strong topology of the corresponding trajectory dynamical systems. By means of generalized Fatou’s lemma we prove the strong convergence of the trajectory attractors of considered systems to the trajectory attractors of the corresponding homogenized reaction–diffusion systems which contain an additional potential. |
| first_indexed | 2024-03-11T06:13:15Z |
| format | Article |
| id | doaj.art-4e495814fb274a2c837572b0e4518cd1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:15Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4e495814fb274a2c837572b0e4518cd12023-11-17T12:28:45ZengMDPI AGMathematics2227-73902023-03-01116144810.3390/math11061448Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic ObstaclesKuanysh A. Bekmaganbetov0Gregory A. Chechkin1Vladimir V. Chepyzhov2Faculty of Mechanics and Mathematics, Kazakhstan Branch of M.V. Lomonosov Moscow State University, Astana 010010, KazakhstanInstitute of Mathematics and Mathematical Modeling, Almaty 050010, KazakhstanInstitute for Information Transmission Problems, Russian Academy of Sciences, 127051 Moscow, RussiaWe study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems in the strong topology of the corresponding trajectory dynamical systems. By means of generalized Fatou’s lemma we prove the strong convergence of the trajectory attractors of considered systems to the trajectory attractors of the corresponding homogenized reaction–diffusion systems which contain an additional potential.https://www.mdpi.com/2227-7390/11/6/1448trajectory attractorshomogenizationreaction–diffusion systemsnon-linear equationsstrong convergence |
| spellingShingle | Kuanysh A. Bekmaganbetov Gregory A. Chechkin Vladimir V. Chepyzhov Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles Mathematics trajectory attractors homogenization reaction–diffusion systems non-linear equations strong convergence |
| title | Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles |
| title_full | Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles |
| title_fullStr | Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles |
| title_full_unstemmed | Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles |
| title_short | Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles |
| title_sort | application of fatou s lemma for strong homogenization of attractors to reaction diffusion systems with rapidly oscillating coefficients in orthotropic media with periodic obstacles |
| topic | trajectory attractors homogenization reaction–diffusion systems non-linear equations strong convergence |
| url | https://www.mdpi.com/2227-7390/11/6/1448 |
| work_keys_str_mv | AT kuanyshabekmaganbetov applicationoffatouslemmaforstronghomogenizationofattractorstoreactiondiffusionsystemswithrapidlyoscillatingcoefficientsinorthotropicmediawithperiodicobstacles AT gregoryachechkin applicationoffatouslemmaforstronghomogenizationofattractorstoreactiondiffusionsystemswithrapidlyoscillatingcoefficientsinorthotropicmediawithperiodicobstacles AT vladimirvchepyzhov applicationoffatouslemmaforstronghomogenizationofattractorstoreactiondiffusionsystemswithrapidlyoscillatingcoefficientsinorthotropicmediawithperiodicobstacles |