Homogenization of a quasilinear elliptic problem in domains with small holes

References

• Chipot M. Elliptic equations: an introductory course. Basel: Birkhäuser Verlag; 2009. (Birkhäuser advanced texts).
   Google Scholar
• Cioranescu D, Donato P, Zaki R. Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions. Asymptot Anal. 2007;53:209–235.
   Web of Science ®Google Scholar
• Cioranescu D, Murat F. Un terme étrange venu d' ailleurs. In: Nonlinear partial differential equations and their applications. Boston: Pitman; 1982. p. 98–138, 154–178. (College de France seminar II & III in: research notes in math.; vol. 60–70).
   Google Scholar
• Conca C, Donato P. Non-homogeneous Neumann problems in domains with small holes. Math Model Numer Anal. 1988;22:561–607.
   Web of Science ®Google Scholar
• Cioranescu D, Damlamian A, Griso G. Periodic unfolding and homogenization. C R Acad Sci Paris Ser 1. 2002;335:99–104.
   Web of Science ®Google Scholar
• Cioranescu D, Damlamian A, Griso G. The periodic unfolding and homogenization. SIAM J Math Anal. 2008;40:1585–1620.
   Web of Science ®Google Scholar
• Damlamian A. Periodic unfolding and homogenization. Acad Sci. 2002;335:99–104.
   Google Scholar
• Damlamian A. An elementary introduction to periodic unfolding. Gakuto Internat Ser Math Sci Appl. 2006;24:119–136.
   Google Scholar
• Cabarrubias B, Donato P. Homogenization of some evolution problems in domains with small holes. Electron J Differ Equ. 2016;169:1–26.
   Google Scholar
• Cioranescu D, Damlamian A, Griso G, et al. The periodic unfolding method for perforated domains and Neumann sieve models. J Math Pure Appl. 2008;89:248–277.
   Web of Science ®Google Scholar
• Cioranescu D, Donato P, Zaki R. Periodic unfolding and Robin problems in perforated domains. C R Math Acad Sci Paris. 2006;342:469–474.
   Web of Science ®Google Scholar
• Cioranescu D, Donato P, Zaki R. The periodic unfolding method in perforated domains. Port Math. 2006;63:467–496.
   Google Scholar
• Cioranescu D, Damlamian A, Donato P, et al. The periodic unfolding method in domains with holes. SIAM J Math Anal. 2012;44(2):718–760.
   Web of Science ®Google Scholar
• Donato P, Le Nguyen KH, Tardieu R. The periodic unfolding method for a class of imperfect transmission problems. J Math Sci. 2011;176:891–927.
   Google Scholar
• Donato P, Yang ZY. The periodic unfolding method for the wave equations in domains with holes. Adv Math Sci Appl. 2012;22:521–551.
   Google Scholar
• Donato P, Yang ZY. The periodic unfolding method for the heat equation in perforated domains. Sci China Math. 2016;59:891–906.
   Web of Science ®Google Scholar
• Ould-Hammouda A, Zaki R. Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes. Carpathian J Math. 2015;31:77–88.
   Web of Science ®Google Scholar
• Cioranescu D, Damlamian A, Griso G. The periodic unfolding method: theory and applications to partial differential equations. Springer Singapore: Springer Nature Singapore Pte Ltd.; 2018.
   Google Scholar
• Bendib S. Homogénéisation d'une classe de problèmes non linéaires avec des conditions de Fourier dans des ouverts perforés [Thèse]. Institut National Polytechnique de Lorraine, France; 2004.
   Google Scholar
• Bendib S, Tcheugoué Tébou RL. Homogénéisation d'une classe de problèmes non linéaires dans des domaines perforés. C R Acad Sci Paris Ser 1. 1999;328:1145–1149.
   Web of Science ®Google Scholar
• Bever MB, editor. Encyclopedia of material science and engineering. Oxford, New York: Pergamon Press; tome 3 (1988), p. 2109, tome 7 (1986), p. 4917–4919, 4950, 5455.
   Google Scholar
• Conca C, Diaz J, Linan A, et al. Homogenization in chemical reactive flows. Electron J Differ Equ. 2004;2004(40):1–22.
   Google Scholar
• Timofte C. On the homogenization of a climatization problem. Stud Univ Babes-Bolyai Math. 2007;52:117–125.
   Google Scholar
• Marchenko VA, Khruslov EYa. Boundary-value problems in domains with fine-grained boundary. Kiev: Naukova Dumka; 1974. Russian.
   Google Scholar
• Marchenko VA, Khruslov EYa. Homogenization of partial differential equations. Basel: Birkhäuser; 2006. (Progress in mathematical physics; 46).
   Google Scholar
• Tartar L. Cours Peccot au Collége De France; 1977. (Partially written in F. Murat and L. Tartar for the H-convergence technique in 1978).
   Google Scholar
• Tartar L. Quelques remarques sur l'homogénéisation in Functional Analysis and Numerical Analysis. Proc. Japan-France Seminar 1976, ed. H. Fujita, Japanese Society for the Promotion of Science, 468–482.
   Google Scholar
• Belyaev AG, Piatnitski AL, Chechkin GA. Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary. Sib Math J. 1998;39(4):621–644. (Translated from Sib Mat Z. 1998;39(4):730–754).
   Web of Science ®Google Scholar
• Belyaev AG, Piatnitski AL, Chechkin GA. Averaging in a perforated domain with an oscillating third boundary condition. Russ Acad Sci Sb Math. 2001;192(7):933–949. (Translated from Mat Sb. 2001;192(7):3–20).
   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
• Onofrei D. The unfolding operator near a hyperplane and its application to the Neumann Sieve model. AMSA. 2006;16:239–258.
   Google Scholar
• Cioranescu D, Ould-Hammouda A. Homogenization of elliptic problems in perforated domains with mixed boundary conditions. Rev Roumaine Math Pures Appl. 2008;53:389–406.
   Google Scholar
• Ould-Hammouda A. Homogenization of a class of Neumann problems in perforated domains. Asymptot Anal. 2011;71:33–57.
   Web of Science ®Google Scholar
• Chechkin GA, Cioranescu D, Damlamian A, et al. On boundary value problem with singular inhomogeneity concentrated on the boundary. J Math Pures Appl. 2012;98(2):115–138.
   Web of Science ®Google Scholar
• Cabarrubias B, Donato P. Homogenization of a quasilinear elliptic problem with nonlinear Robin boundary conditions. Appl Anal. 2012;91:1111–1127.
   Web of Science ®Google Scholar
• Cardone G, D'Apice C, De Maio U. Homogenization in perforated domains with mixed conditions. Nonlinear Differ Equ Appl. 2002;9:325–346.
   Web of Science ®Google Scholar
• Corbo Esposito A, D'Apice C, Gaudiello A. Homogenization in a perforated domain with both Dirichlet and Neumann boundary conditions on small holes. Asymptot Anal. 2002;31:297–316.
   Web of Science ®Google Scholar
• Casado-Diaz J. Two-scale convergence for nonlinear Dirichlet problems in perforated domains. Proc R Soc Edinb. 2000;130:249–276.
   Google Scholar
• Casado-Diaz J, Luna-Leynez M, Martin JD. An adaptation of the multiscale methods for the analysis of very thin reticulated structures. C R Acad Sci Paris. 2001;332:223–228.
   Web of Science ®Google Scholar
• Cabarrubias B, Donato P. Existence and uniqueness for a quasilinear elliptic problem with nonlinear Robin conditions. Carpathian J Math. 2011;27:173–184.
   Web of Science ®Google Scholar
• Bensoussan A, Lions J-L, Papanicolaou G. Asymptotic analysis for periodic structures. Amsterdam: North Holland; 1978.
   Google Scholar
• Avila J. Homogenization of some boundary value problems in perforated domains [master's thesis]. University of the Philippines Diliman, Philippines; 2019.
   Google Scholar