1. Y. Amirat, G.A. Chechkin, R.R. Gadyl’shin. Asymptotics of simple eigenvalues and eigenfunctions for the laplace operator in a domain with oscillating boundary // Comput. Math. Math. Phys. 46:1, 97-110 (2006). DOI: 10.1134/S0965542506010118 EDN: LKCBNH
2. Y. Amirat, G.A. Chechkin, R.R. Gadyl’shin. Asymptotics for eigenelements of laplacian in domain with oscillating boundary: multiple eigenvalues // Appl. Anal. 86:7, 873-897 (2007). DOI: 10.1080/00036810701461238 EDN: WTHLYE
3. Y. Amirat, G.A. Chechkin, R.R. Gadyl’shin. Asymptotics of the solution of a Dirichlet spectral problem in a junction with highly oscillating boundary // C. R., Méc., Acad. Sci. Paris 336:9, 693-698 (2008). DOI: 10.1016/j.crme.2008.06.008
4. Y. Amirat, G.A. Chechkin, R.R. Gadyl’shin. Spectral boundary homogenization in domains with oscillating boundaries // Nonlinear Anal., Real World Appl. 11:6, 4492-4499 (2010). DOI: 10.1016/j.nonrwa.2008.11.023
5. G.F. Azhmoldaev, K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov. Homogenization of attractors to reaction-diffusion equations in domains with rapidly oscillating boundary: critical case // Netw. Heterog. Media 19:3, 1381-1401 (2024). DOI: 10.3934/nhm.2024059
6. A.V. Babin, M.I. Vishik. Attractors of Evolution Equations // North-Holland, Amsterdam (1992).
7. K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov. Weak convergence of attractors of reaction-diffusion systems with randomly oscillating coefficients // Appl. Anal. 98:1-2, 256-271 (2019). DOI: 10.1080/00036811.2017.1400538 EDN: AXZXPL
8. K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov. “Strange term” in homogenization of attractors of reaction-diffusion equation in perforated domain // Chaos Solitons Fractals 140, 110208 (2020). DOI: 10.1016/j.chaos.2020.110208 EDN: CNOORU
9. K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov, A.A. Tolemis. Homogenization of attractors to Ginzburg - Landau equations in media with locally periodic obstacles: critical case // Bull. Karaganda Univ. Math. Series 3(111), 11-27 (2023). DOI: 10.31489/2023m3/11-27
10. K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov. Homogenization of random attractors for reaction-diffusion systems // C. R., Méc., Acad. Sci. Paris. 344:11-12, 753-758 (2016). DOI: 10.1016/j.crme.2016.10.015
11. K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov, A.Yu. Goritsky. Homogenization of trajectory attractors of 3D Navier - Stokes system with randomly oscillating force // Discrete Contin. Dyn. Syst. 37:5, 2375-2393 (2017). DOI: 10.3934/dcds.2017103 EDN: YVOVFT
12. A.G. Belyaev, A.G. Mikheev, A.S. Shamaev. Diffraction of a plane wave by a rapidly-oscillating surface // Comput. Math. Math. Phys. 32:8, 1121-1133 (1992). EDN: ZZXOCZ
13. A.G. Belyaev, A.L. Piatnitski, G.A. Chechkin. Asymptotic behavior of solution for boundary-value problem in a perforated domain with oscillating boundary // Siberian Math. J. 39:4, 730-754 (1998). DOI: 10.1007/BF02673049 EDN: ZDBXQQ
14. D. Borisov, G. Cardone, L. Faella, C. Perugia. Uniform resolvent convergence for strip with fast oscillating boundary // J. Differ. Equations 255:12, 4378-4402 (2013). DOI: 10.1016/j.jde.2013.08.005
15. D.I. Borisov. Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions // J. Math. Sci. (N.Y.), 264:5, 562-580 (2022). DOI: 10.1007/s10958-022-06017-1 EDN: DFNQOV
16. D.I. Borisov, R.R. Suleimanov. On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary // Math. Notes, 116:2, 182-199 (2024). DOI: 10.1134/S0001434624070149
17. G.A. Chechkin, A.L. Piatnitski. Homogenization of boundary-value problem in a locally periodic perforated domain // Appl. Anal. 71:1-4, 215-235 (1999). DOI: 10.1080/00036819908840714
18. G.A. Chechkin, A. Friedman, A.L. Piatnitski. The boundary-value problem in domains with very rapidly oscillating boundary // J. Math. Anal. Appl. 231:1, 213-234 (1999). DOI: 10.1006/jmaa.1998.6226 EDN: LFIORT
19. G.A. Chechkin, A.L. Piatnitski, A.S. Shamaev. Homogenization. Methods and Applications. Amer. Math. Soc., Providence, RI (2007).
20. G.A. Chechkin, Yu.O. Koroleva, L.-E. Persson. On the precise asymptotics of the constant in the Friedrich’s inequality for functions, vanishing on the part of the boundary with microinhomogeneous structure // J. Inequal. Appl. 2007, 034138 (2007). DOI: 10.1155/2007/34138
21. G.A. Chechkin, Yu.O. Koroleva, A. Meidell, L.E. Persson. On the Friedrichs inequality in a domain perforated along the boundary. Homogenization procedure. Asymptotics in parabolic problems // Russ. J. Math. Phys. 16:1, 1-16 (2009). DOI: 10.1134/S1061920809010014
22. T.A. Mel’nyk, G.A. Chechkin. Homogenization of a boundary-value problem in a thick three-dimensional multilevel junction // Mat. Sb. 200:3, 49-74 (2009). [Sb. Math. 200:3, 357-383 (2009).]. DOI: 10.1070/SM2009v200n03ABEH004000 EDN: QBFVDD
23. G.A. Chechkin, T.P. Chechkina, C. D’Apice, U. De Maio, T.A. Mel’nyk. Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone // Appl. Anal. 88:10-11, 1543-1562 (2009). DOI: 10.1080/00036810902994268 EDN: MWZQRR
24. G.A. Chechkin, V.V. Chepyzhov, L.S. Pankratov. Homogenization of trajectory attractors of Ginzburg - Landau equations with randomly oscillating terms // Discrete Contin. Dyn. Syst., Ser. B 23:3, 1133-1154 (2018). DOI: 10.3934/dcdsb.2018145
25. V.V. Chepyzhov, M.I. Vishik. Trajectory attractors for reaction-diffusion systems // Topol. Methods Nonlinear Anal. 7:1, 49-76 (1996). DOI: 10.12775/TMNA.1996.002
26. V.V. Chepyzhov, M.I. Vishik. Attractors for Equations of Mathematical Physics. Amer. Math. Soc., Providence, RI (2002).
27. M. Efendiev, S. Zelik. Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization // Ann. Inst. Henri Poincaré, Anal. Non Linéaire 19:6, 961-989 (2002). DOI: 10.1016/s0294-1449(02)00115-4
28. A. Gaudiello, A. Sili. Homogenization of highly oscillating boundaries with strongly contrasting diffusivity // SIAM J. Math. Anal. 47:3, 1671-1692 (2015). DOI: 10.1137/140987225
29. V.V. Grushin, S.Yu. Dobrokhotov, Homogenization in the problem of long water waves over a bottom site with fast oscillations // Math. Notes. 95:3, 324-337 (2014). DOI: 10.1134/S0001434614030055
30. J.K. Hale, S.M. Verduyn Lunel. Averaging in infinite dimensions // J. Integral Equations Appl. 2:4, 463-494 (1990). DOI: 10.1216/jiea/1181075583
31. A.A. Ilyin. Averaging principle for dissipative dynamical systems with rapidly oscillating right- hand sides // Sb. Math. 187:5, 635-677 (1996). DOI: 10.1070/SM1996v187n05ABEH000126 EDN: LOFISN
32. V.V. Jikov, S.M. Kozlov, O.A. Oleinik. Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin (1994).
33. V.A. Kozlov, S.A. Nazarov, The spectrum asymptotics for the Dirichlet problem in the case of the biharmonic operator in a domain with highly indented boundary // St. Petersburg Math. J. 22:6, 941-983 (2011). DOI: 10.1090/S1061-0022-2011-01178-1
34. J.-L. Lions. Quelques méthodes de résolutions des problémes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1969).
35. V.A. Marchenko, E.Ya. Khruslov. Homogenization of Partial Differential Equations. Birkhäuser, Boston, MA (2006). DOI: 10.1007/978-0-8176-4468-0
36. A. McMillan, R. Jones, D. Peng, G.A. Chechkin. A computational study of the influence of surface roughness on material strength // Meccanica. 53:9, 2411-2436 (2018). DOI: 10.1007/s11012-018-0830-6 EDN: UYAOKQ
37. N. Neuss, M. Neuss-Radu, A. Mikelić, Effective laws for the Poisson equation on domains with curved oscillating boundaries // Appl. Anal. 85:5, 479-502 (2006). DOI: 10.1080/00036810500340476 EDN: ARRCOZ
38. O.A. Oleinik, A.S. Shamaev, G.A. Yosifian. Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam (1992). EDN: UCSUGD
39. E. Sanchez-Palencia. Homogenization Techniques for Composite Media // Springer-Verlag, Berlin (1987). DOI: 10.1007/3-540-17616-0
40. R. Temam. Infinite-dimensional dynamical systems in mechanics and physics. Springer-Verlag, New York (1988).