Attractors of Ginzburg–Landau equations with oscillating terms in porous media: homogenization procedure

References

• Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. Attractors and a ‘strange term’ in homogenized equation. C R Mec. 2020;348(5):351–359.
   Web of Science ®Google Scholar
• Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. ‘Strange term’ in homogenization of attractors of reaction–diffusion equation in perforated domain. Chaos Solit Fractals. 2020;140:Article ID 110208.
   Web of Science ®Google Scholar
• Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. On attractors of reaction–diffusion equations in a porous orthotropic medium. Russ Acad Sci Dokl Math. 2021;103(3):103–107. (Translated from Doklady Akademii Nauk. 2021;498(3): 10–15).
   Google Scholar
• Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. Homogenization of attractors of reaction–diffusion system with rapidly oscillating terms in an orthotropic porous medium. J Math Sci. 2021;259(2):148–166. (Translated from Problemy mat Analiza. 2021;112:35–50).
   Google Scholar
• Belyaev AG, Piatnitski AL, Chechkin GA. Asymptotic behavior of solution for boundary-value problem in a perforated domain with oscillating boundary. Sib Math J. 1998;39(4):730–754.
   Web of Science ®Google Scholar
• Cioranescu D, Murat F. Un terme étrange venu d'ailleurs I & II. In: Berzis H, Lions JL, editors. Nonlinear Partial Differential Equations and their Applications. Collège de France Seminar, Volume II & III. Research Notes in Mathematics, 60 & 70, London: Pitman; 1982. p. 98–138 & 154–178.
   Google Scholar
• Marchenko VA, Khruslov EY. Boundary value problems in domains with fine-grain boundary. Kiev: Naukova Dumka; 1974. (in Russian).
   Google Scholar
• Chechkin GA, Piatnitski AL, Shamaev AS. Homogenization: methods and applications. Providence (RI): American Mathematical Society; 2007.
   Google Scholar
• Jikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators and integral functionals. Berlin: Springer; 1994.
   Google Scholar
• Oleinik OA, Shamaev AS, Yosifian GA. Mathematical problems in elasticity and homogenization. Amsterdam: Elsevier; 1992.
   Google Scholar
• Sanchez-Palencia É. Homogenization techniques for composite media. Berlin: Springer; 1987.
   Google Scholar
• Babin AV, Vishik MI. Attractors of evolution equations. Amsterdam: Elsevier; 1992.
   Google Scholar
• Chepyzhov VV, Vishik MI. Attractors for equations of mathematical physics. Providence (RI): American Mathematical Society; 2002.
   Google Scholar
• Temam R. Infinite-dimensional dynamical systems in mechanics and physics. New York (NY): Springer; 1988. (Applied Mathematics Series; 68).
   Google Scholar
• Efendiev M, Zelik S. Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Ann Inst H Poincaré Anal Non Linéaire. 2002;19:961–989.
   Web of Science ®Google Scholar
• Hale JK, Verduyn Lunel SM. Averaging in infinite dimensions. J Int Equ Appl. 1990;2:463–494.
   Google Scholar
• Ilyin AA. Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides. Sb Math. 1996;187:635–677.
   Web of Science ®Google Scholar
• Bekmaganbetov KA, Chechkin GA, Chepyzhov VV. Weak convergence of attractors of reaction–diffusion systems with randomly oscillating coefficients. Appl Anal. 2019;98(1–2):256–271.
   Web of Science ®Google Scholar
• Chechkin GA, Chepyzhov VV, Pankratov LS. Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms. Discrete Continuous Dyn Syst Ser B. 2018;23(3):1133–1154.
   Web of Science ®Google Scholar
• Boyer F, Fabrie P. Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. New York (NY): Springer; 2013. (Applied Mathematical Sciences; 183).
   Google Scholar
• Mikhailov VP. Partial differential equations. Translated from the Russian by P. C. Sinha. Moscow: Mir, Chicago (IL): distributed by Imported; 1978.
   Google Scholar
• Belyaev AG, Piatnitski AL, Chechkin GA. Averaging in a perforated domain with an oscillating third boundary condition. Sb Math. 2001;192(7):933–949.
   Web of Science ®Google Scholar
• Lions J-L. Quelques méthodes de résolutions des problèmes aux limites non linéaires. Paris: Dunod, Gauthier-Villars; 1969.
   Google Scholar
• Diaz JI, Gomez-Castro D, Shaposhnikova TA, et al. Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles. Appl Anal. 2018;98(1–2):232–255.
   Web of Science ®Google Scholar
• Chechkin GA, Piatnitski AL. Homogenization of boundary-value problem in a locally periodic perforated domain. Appl Anal. 1999;71(1–4):215–235.
   Google Scholar
• Chepyzhov VV, Vishik MI. Trajectory attractors for reaction-diffusion systems. Top Meth Nonlinear Anal J Julius Schauder Center. 1996;7(1):49–76.
   Google Scholar
• Chepyzhov VV, Goritsky AY., Vishik MI. Integral manifolds and attractors with exponential rate for nonautonomous hyperbolic equations with dissipation. Russ J Math Phys. 2005;12:17–39.
   Web of Science ®Google Scholar
• Chepyzhov VV, Vishik MI, Wendland WL. On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging. Discrete Contin Dyn Syst. 2005;12:27–38.
   Web of Science ®Google Scholar
• Vishik MI, Chepyzhov VV. Approximation of trajectories lying on a global attractor of a hyperbolic equation with an exterior force that oscillates rapidly over time. Sb Math. 2003;194:1273–1300.
   Web of Science ®Google Scholar
• Zelik S. Global averaging and parametric resonances in damped semilinear wave equations. Proc R Soc Edinb A. 2006;136:1053–1097.
   Google Scholar