Free Access
Issue
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
Page(s) 1429 - 1463
DOI https://doi.org/10.1051/m2an/2020001
Published online 26 June 2020
  1. Y. Achdou and N. Tchou, Hamilton-Jacobi equations on networks as limits of singularly perturbed problems in optimal control: dimension reduction. Comm. Partial Differ. Equ. 40 (2015) 652–693. [CrossRef] [Google Scholar]
  2. A.K. Al Sayed, G. Carbou and S. Labbé, Asymptotic model for twisted bent ferromagnetic wires with electric current. Z. Angew. Math. Phys. 70 (2019) 6. [Google Scholar]
  3. Y. Amirat and R. Touzani, A circuit equation as a limit of eddy current. Arch. Ration. Mech. Anal. 226 (2017) 405–440. [Google Scholar]
  4. J. Ballato and M.C. Gupta, The Handbook of photonics, 2nd edition, edited V. Gopalan, K.L. Schepler, V. Dierolf, I. Biaggio. In: Chapter 6. Ferroelectric Materials. CRC Press (2006). [Google Scholar]
  5. A. Braides, Γ-convergence for beginners. In: Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). [Google Scholar]
  6. R. Bunoiu, A. Gaudiello and A. Leopardi, Asymptotic analysis of a Bingham fluid in a thin T-like shaped structure. J. Math. Pures Appl. 123 (2019) 148–166. [Google Scholar]
  7. L. Carbone, K. Chacouche and A. Gaudiello, Fin junction of ferroelectric thin films. Adv. Calc. Var. 11 (2018) 341–371. [CrossRef] [Google Scholar]
  8. L. Carbone and R. De Arcangelis, Unbounded functionals in the calculus of variations. Representation, relaxation, and homogenization. In: Vol. 125 of Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, FL (2002). [Google Scholar]
  9. G. Carbou and S. Labbé, Stabilization of walls for nano-wires of finite length. ESAIM: COCV 18 (2012) 1–21. [CrossRef] [EDP Sciences] [Google Scholar]
  10. K. Chacouche, L. Faella and C. Perugia, Quasi-stationary ferromagnetic problem for thin multi-structures. Rev. Mat. Complut. 30 (2017) 657–685. [Google Scholar]
  11. K. Chacouche, L. Faella and C. Perugia, Junction of quasi-stationary ferromagnetic wires. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31 (2020) 25–56. [CrossRef] [Google Scholar]
  12. P. Chandra and P.B. Littlewood, A Landau primer for ferroelectrics, edited by K. Rabe, C.H. Ahn and J.-M. Triscone. In: The Physics of Ferroelectrics: A Modern Perspective. In: Vol. 105 of Topics Appl Phys (2007), 69–116. [CrossRef] [Google Scholar]
  13. P.G. Ciarlet, Linear and nonlinear functional analysis with applications, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2013. [Google Scholar]
  14. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979) 315–344. [Google Scholar]
  15. M. Costabel, M. Dauge and S. Nicaise, Singularities of Maxwell interface problems, ESAIM: M2AN 33 (1999) 627–649. [CrossRef] [EDP Sciences] [Google Scholar]
  16. L.E. Cross and R.E. Newnham, History of ferroelectrics. Reprinted from the Ceramics and Civilization. In: Vol. III of High-Technology Ceramics-Past, Present, and Future. The American Ceramic Society Inc (1987). [Google Scholar]
  17. G. Dal Maso, An introduction to Γ-convergence. In: Vol. 8 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston Inc, Boston, MA (1993). [Google Scholar]
  18. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975) 842–850. [MathSciNet] [Google Scholar]
  19. A. Gaudiello, D. Gómez and M.E. Pérez, Asymptotic analysis of the high frequencies for the Laplace operator in a thin T-like shaped structure. J. Math. Pures Appl. 134 (2020) 299–327. [Google Scholar]
  20. A. Gaudiello and R. Hadiji, Junction of one-dimensional minimization problems involving S2 valued maps. Adv. Differ. Equ. 13 (2008) 935–958. [Google Scholar]
  21. A. Gaudiello and R. Hadiji, Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S2. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 59–80. [CrossRef] [Google Scholar]
  22. A. Gaudiello and R. Hadiji, Junction of ferromagnetic thin films. Calc. Var. Partial Differ. Equ. 39 (2010) 593–619. [Google Scholar]
  23. A. Gaudiello and R. Hadiji, Ferromagnetic thin multi-structures. J. Differ. Equ. 257 (2014) 1591–1622. [Google Scholar]
  24. A. Gaudiello and K. Hamdache, The polarization in a ferroelectric thin film: local and nonlocal limit problems. ESAIM: M2AN 19 (2013) 657–667. [Google Scholar]
  25. A. Gaudiello and K. Hamdache, A reduced model for the polarization in a ferroelectric thin wire. NoDEA Nonlinear Differ. Equ. Appl. 22 (2015) 1883–1896. [CrossRef] [Google Scholar]
  26. A. Goussev, R.G. Lund and J.M. Robbins, V. Slastikov, C. Sonnenberg, Domain wall motion in magnetic nanowires: an asymptotic approach. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2013) 20130308. [CrossRef] [Google Scholar]
  27. H. Le Dret, Problèmes variationnels dans le multi-domaines: modélisation des jonctions et applications. In: Vol. 19 of Research in Applied Mathematics. Masson, Paris (1991). [Google Scholar]
  28. T. Mitsui, I. Taksuzaki and E. Nakamura, An Introduction to the Physics of Ferroelectrics. Gordon and Breach, London, New York (1976). [Google Scholar]
  29. A. Romano and E.S. Suhubi, Structure of Weis domain in ferroelectric crystals. Int. J. Eng. Sci. 30 (1992) 1715–1729. [Google Scholar]
  30. D. Sanchez, Behaviour of the Landau-Lifschitz equation in a ferromagnetic wire. Math. Methods Appl. Sci. 32 (2009) 167–205. [Google Scholar]
  31. V. Slastikov and C. Sonnenberg, Reduced models for ferromagnetic nanowires. IMA J. Appl. Math. 77 (2012) 220–235. [Google Scholar]
  32. Y. Su and C.M. Landis, Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J. Mech. Phys. Solids 55 (2007) 280–305. [Google Scholar]
  33. W. Zhang and K. Bhattacharya, A computational model of ferroelectric domains. Part I. Model formulation and domain switching. Acta Mater. 53 (2005) 185–198. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you