Homogenization results for a Landau–Lifshitz–Gilbert equation in composite materials with transmission defects

References

• Bakhvalov N, Panasenko G. Homogenization: averaging processes in periodic media. Dordrecht: Kluwer; 1989.
   Google Scholar
• Bensoussan A, Lions JL, Papanicolaou G. Asymptotic analysis for periodic structures. Amsterdam: North-Holland; 1978.
   Google Scholar
• Landauer R. Electrical conductivity in inhomogeneous media. AIP Conf Proc. 1978;40(2):2–45.
   Google Scholar
• Alouges F, Di Fratta G. Homogenization of composite ferromagnetic materials. Proc R Soc A. 2015;471:20150365.
   Google Scholar
• Haddar H, Joly P. Homogenized model for a laminar ferromagnetic medium. Proc R Soc Edinb, Sect A, Math. 2003;133(3):567–598.
   Google Scholar
• Choquet C, Moumni M, Tilioua M. Homogenization of the Landau–Lifshitz–Gilbert equation in a contrasted composite medium. Discrete Cont Dyn-S. 2018;133(1):35–57.
   Google Scholar
• Leitenmaier L, Runborg O. Homogenization of the Landau–Lifshitz equation. arXiv preprint, arXiv:2012.12567, 2020.
   Google Scholar
• Lipton R, Vernescu B. Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface. Math Models Methods Appl Sci. 1995;5(8):1139–1173.
   Web of Science ®Google Scholar
• Neuss-Radu M, Ludwig S, Jäger W. Multiscale analysis and simulation of a reaction-diffusion problem with transmission conditions. Nonlinear Anal Real World Appl. 2010;11(6):4572–4585.
   Web of Science ®Google Scholar
• Monsurrò S. Homogenization of a two-component composite with interfacial thermal barrier. Adv Math Sci Appl. 1992;13(1):43–63.
   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
• Cioranescu D, Donato P. An introduction to homogenization. Oxford: Oxford University Press; 1999. (Oxford Lecture Series in Mathematics and Applications, 17).
   Google Scholar
• Cioranescu D, Donato P, Zaki R. The periodic unfolding method in perforated domains. Port. Math. (N.S.). 2006;63:467–496.
   Google Scholar
• Cioranescu D, Damlamian A, Griso G. The periodic unfolding method in homogenization. SIAM J Math Anal. 2008;40(4):1585–1620.
   Web of Science ®Google Scholar
• Yang Z. Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method. Com Pure Appl Anal. 2014;13(1):249–272.
   Web of Science ®Google Scholar
• Yang Z. The periodic unfolding method for a class of parabolic problems with imperfect interfaces. ESAIM-Math Model Num Anal. 2014;48:1279–1302.
   Web of Science ®Google Scholar
• Acerbi E, Chiado Piat V, Dal Maso G, et al. An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal Theory Methods Appl. 1992;18(5):481–496.
   Web of Science ®Google Scholar
• Mabrouk M, Hassan S. Homogenization of a composite medium with a thermal barrier. Math Methods Appl Sci. 2004;27:405–425.
   Web of Science ®Google Scholar
• Damlamian A, Donato P. Which sequences of holes are admissible for periodic homogenization with neumann boundary condition?. ESAIM-Control Optim Calc Var. 2002;8:555–585.
   Web of Science ®Google Scholar
• Alouges F, Soyeur D. On global weak solutions for Landau–Lifshitz equations: existence and nonuniqueness. Nonlinear Anal Theory Methods Appl. 1992;18(11):1071–1084.
   Web of Science ®Google Scholar
• Ammari H, Halpern L, Hamdache K. Thin ferromagnetic films. Asympt Anal. 2000;24:277–294.
   Web of Science ®Google Scholar
• Di Fratta G, Muratov CB, Rybakov FN, et al. Variational principles of micromagnetics revisited. SIAM J Math Anal. 2020;52(4):3580–3599.
   Web of Science ®Google Scholar
• Hamdache K, Tilioua M. On the zero thickness limit of thin ferromagnetic films with surface anisotropy energy. Math Models Methods Appl Sci. 2001;11:1469–1490.
   Web of Science ®Google Scholar
• Casado-Díaz J. Two-scale convergence for nonlinear Dirichlet problems in perforated domains. Proc R Soc Edinb. 2000;130A:249–276.
   Google Scholar
• Dautray R, Lions PL. Mathematical analysis and numerical methods for science and technology. Vol. 4. Berlin: Springer Verlag; 1999.
   Google Scholar