References
- Gómez D, Pérez ME, Shaposhnikova TA. On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems. Asymp Anal. 2012;80:289–322.
- Cioranescu D, Murat F. A strange term coming from nowhere. In: Cherkaev A, Kohn R, editors. Topics in the mathematical modelling of composite materials. Progress in nonlinear differential equations and their applications. Vol. 31. Boston: Birkäuser; 1997. p. 45–93.
- Marchenko VA, Khruslov EY. Homogenization of partial differential equations, Progress in mathematical physics. Vol. 46. Boston (MA): Birkhäuser Boston; 2006.
- Sanchez-Palencia E. Boundary value problems in domains containing perforated wall. In: Brezis H, Lions JL, editors. Nonlinear partial differential equations and their applications, Collège de France Seminar, Vol. III. Research notes in mathematics. Vol. 70. Boston: Pitman; 1982. p. 309–325.
- Lobo M, Pérez ME, Sukharev VV, et al. Averaging of boundary-value problem in domain perforated along (n-1) - dimensional manifold with nonlinear third type boundary conditions on the boundary of cavities. Dokl Math. 2011;83:34–38.
- Brillard A, Gómez D, Lobo M, et al. Boundary homogenization in perforated domains for adsorption problems with an advection term. Appl Anal. 2016;95:218–237.
- Gómez D, Lobo M, Pérez ME, et al. Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds. Appl Anal. 2013;92:218–237.
- Gómez D, Pérez ME, Shaposhnikova TA. Spectral boundary homogenization problems in perforated domains with Robin boundary conditions and large parameters. In: Constanda C, Bodmann BEJ, de Campos Velho HF, editors. Integral methods in science and engineering. New York (NY): Birkhäuser/Springer; 2013. p. 155–174.
- Gómez D, Pérez ME, Shaposhnikova TA. On correctors for spectral problems in the homogenization of Robin boundary conditions with very large parameters. Int J Appl Math. 2013;26:309–320.
- Allaire G. Homogenization of the Naviers--Stokes equations in open sets perforated with tiny holes II. Non critical size of the holes for a volume distribution of holes and a surface distribution of holes. Arch Ration Mech Anal. 1983;113:261–298.
- Brillard A. Asymptotic flow of a viscous and incompressible fluid through a plane sieve. In: Bandle C, Bemelmans J, Chipot M, et al., editors. Progress in partial differential equations: calculus of variations, applications, Pitman research notes in mathematics series. Vol. 267. Harlow: Longman Scientific & Technical; 1992. p. 158–172.
- Conca C. Étude d’un fluide traversant une paroi perforée. I. Comportement limite près de la paroi. [Study of fluid flow through a perforated barrier. I. Limit behavior near the barrier]. J Math Pures Appl. 1987;66:1–43.
- Conca C. Étude d’un fluide traversant une paroi perforée. II. Comportement limite loin de la paroi [Study of fluid flow through a perforated barrier. II. Limit behavior away from the barrier]. J Math Pures Appl. 1987;66:45–70.
- Sanchez-Hubert J, Sanchez-Palencia E. Acoustic fluid flow through holes and permeability of perforated walls. J Math Anal Appl. 1982;87:427–453.
- Sanchez-Palencia E. Un problème d’ecoulement lent d’un fluide incompressible au travers d’une paroi finement perforée. In: Bergman D, Lions JL, Papanicolaou G, et al., editors. Homogenization methods: theory and applications in physics, Collect Dir Études Rech Élec France. Vol. 57. Paris: Eyrolles; 1985. p. 371–400.
- Lobo M, Pérez E. Asymptotic behaviour of an elastic body with a surface having small stuck regions. RAIRO Modél Math Anal Numér. 1988;22:609–624.
- Ladyzhenskaya OA. The mathematical theory of viscous incompressible flow, Mathematics and its applications. Vol. 2. New York (NY): Gordon and Breach Science Publishers; 1969.
- Temam R. Navier--Stokes equations Theory and numerical analysis. Studies in mathematics and its applications. Vol. 2. Amsterdam: North-Holland; 1979.
- Lions JL. Quelques méthodes de résolution des problémes aux limites non linéaires. Paris: Dunod; 1969.
- Brezis H. Problèmes unilatéraux. J Math Pures Appl. 1972;51:1–168.
- Germain P. Mécanique Tomes I and II École polytechnique. Paris: Ellipses; 1986.
- Nguetseng N, Sanchez-Palencia E. Stress concentration for defects distributed near a surface. In: Ladevèze P, editor. Local effects in the analysis of structures, Stud Appl Mech. Vol. 12. Amsterdam: Elsevier; 1985. p. 55–74.
- Dauge M. Stationary Stokes and Navier--Stokes systems on two- or three-dimensional domains with corners I Linearized equations. SIAM J Math Anal. 1989;20(1):74–97.
- Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Recherches en mathématiques appliquées. Vol. 5. Paris: Masson; 1987.
- Kondratiev VA, Oleinik OA. Boundary value problems for partial differential equations in nonsmooth domains. Russ Math Surv. 1983;38(2):1–86.
- Sanchez-Hubert J, Sanchez-Palencia E. Vibration and coupling of continuous systems. Asymptotic methods. Heidelberg: Springer; 1989.
- Brillard A, Lobo M, Pérez E. Homogénéisation de frontières par épi-convergence en élasticité linéaire. [Homogenization of boundaries by epiconvergence in linear elasticity]. RAIRO Modél Math Anal Numér. 1990;24:5–26.
- Sanchez-Hubert J, Sanchez-Palencia E. Coques Élastiques minces propriétés asympotiques. Paris: Masson; 1997.
- Nazarov SA, Sokolowski J, Specovius-Neugebauer M. Polarization matrices in anisotropic heterogeneous elasticity. Asymp Anal. 2010;68(4):189–221.
- Lobo M, Pérez E. On vibrations of a body with many concentrated masses near the boundary. Math Model Meth Appl Sci. 1993;3:249–273.
- Hornung U. Homogenization and porous media. New York (NY): Springer-Velag; 1997.
- Kaizu S. The Poisson equation with semilinear boundary conditions in domains with many tiny holes. J Fac Sci Univ Tokyo Sec IA Math. 1989;36:43–86.
- Goncharenko M. The asymptotic behaviour of the third boundary-value problem solutions in domains with fine-grained boundaries. In: Cioranescu D, Damlamian A, Donato P, editors. Homogenization and applications to material sciences, GAKUTO international series, Mathematical sciences and applications. Vol. 9. Tokyo: Gakkotosho; 1995. p. 203–213.
- Gómez D, Lobo M, Pérez ME, et al. Unilateral problems for the p-Laplace operator in perforated media involving large parameters. ESAIM Control Optim Calc Var. 2017. DOI:10.1051/cocv/2017026
- Pérez E, Shaposhnikova TA, Zubova MN. A homogenization problem in a domain perforated by tiny isoperimetric holes with nonlinear Robin type boundary conditions. Dokl Math. 2014;90:489–494.
- Kaizu S. The Poisson equation with nonautonomous semilinear boundary conditions in domains with many time holes. SIAM J Math Anal. 1991;22:1222–1245.