September  2010, 9(5): 1345-1361. doi: 10.3934/cpaa.2010.9.1345

Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients


Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050, UFR des Sciences et Technologie, 61, Avenue du Général de Gaulle, P3, 4e étage, 94010 Créteil Cedex, France


Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe, 657-8501, Japan

Received  August 2009 Revised  November 2009 Published  May 2010

In this paper, a class of minimization problems, associated with the micromagnetics of thin films, is dealt with. Each minimization problem is distinguished by the thickness of the thin film, denoted by $ 0 < h < 1 $, and it is considered under spatial indefinite and degenerative setting of the material coefficients. On the basis of the fundamental studies of the governing energy functionals, the existence of minimizers, for every $ 0 < h < 1 $, and the 3D-2D asymptotic analysis for the observing minimization problems, as $ h \to 0 $, will be demonstrated in the main theorem of this paper.
Citation: Rejeb Hadiji, Ken Shirakawa. Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1345-1361. doi: 10.3934/cpaa.2010.9.1345

Rejeb Hadiji, Ken Shirakawa. 3D-2D asymptotic observation for minimization problems associated with degenerate energy-coefficients. Conference Publications, 2011, 2011 (Special) : 624-633. doi: 10.3934/proc.2011.2011.624


Mustapha El Jarroudi, Youness Filali, Aadil Lahrouz, Mustapha Er-Riani, Adel Settati. Asymptotic analysis of an elastic material reinforced with thin fractal strips. Networks and Heterogeneous Media, 2022, 17 (1) : 47-72. doi: 10.3934/nhm.2021023


Makram Hamouda, Chang-Yeol Jung, Roger Temam. Asymptotic analysis for the 3D primitive equations in a channel. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 401-422. doi: 10.3934/dcdss.2013.6.401


Xiao-Ping Wang, Ke Wang, Weinan E. Simulations of 3-D domain wall structures in thin films. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 373-389. doi: 10.3934/dcdsb.2006.6.373


Michael V. Klibanov, Dinh-Liem Nguyen, Loc H. Nguyen, Hui Liu. A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data. Inverse Problems and Imaging, 2018, 12 (2) : 493-523. doi: 10.3934/ipi.2018021


Thomas März, Andreas Weinmann. Model-based reconstruction for magnetic particle imaging in 2D and 3D. Inverse Problems and Imaging, 2016, 10 (4) : 1087-1110. doi: 10.3934/ipi.2016033


Juan Manuel Reyes, Alberto Ruiz. Reconstruction of the singularities of a potential from backscattering data in 2D and 3D. Inverse Problems and Imaging, 2012, 6 (2) : 321-355. doi: 10.3934/ipi.2012.6.321


A. Naga, Z. Zhang. The polynomial-preserving recovery for higher order finite element methods in 2D and 3D. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 769-798. doi: 10.3934/dcdsb.2005.5.769


Gerhard Kirsten. Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations. Journal of Computational Dynamics, 2022, 9 (2) : 159-183. doi: 10.3934/jcd.2021025


Thomas Y. Hou, Danping Yang, Hongyu Ran. Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1153-1186. doi: 10.3934/dcds.2005.13.1153


S. E. Pastukhova. Asymptotic analysis in elasticity problems on thin periodic structures. Networks and Heterogeneous Media, 2009, 4 (3) : 577-604. doi: 10.3934/nhm.2009.4.577


Ciro D’Apice, Umberto De Maio, T. A. Mel'nyk. Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2. Networks and Heterogeneous Media, 2007, 2 (2) : 255-277. doi: 10.3934/nhm.2007.2.255


Xiaoli Lu, Pengzhan Huang, Yinnian He. Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 815-845. doi: 10.3934/dcdsb.2020143


Kush Kinra, Manil T. Mohan. Convergence of random attractors towards deterministic singleton attractor for 2D and 3D convective Brinkman-Forchheimer equations. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021061


Patrick Fischer, Charles-Henri Bruneau, Hamid Kellay. Multiresolution analysis for 2D turbulence. part 2: A physical interpretation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 717-734. doi: 10.3934/dcdsb.2007.7.717


G. Deugoué, T. Tachim Medjo. The Stochastic 3D globally modified Navier-Stokes equations: Existence, uniqueness and asymptotic behavior. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2593-2621. doi: 10.3934/cpaa.2018123


Zijun Chen, Shengkun Wu. Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4307-4319. doi: 10.3934/cpaa.2021161


Huimin Liang, Peixuan Weng, Yanling Tian. Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1471-1495. doi: 10.3934/cpaa.2016.15.1471


Bo-Qing Dong, Zhi-Min Chen. Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 765-784. doi: 10.3934/dcds.2009.23.765


Chaoying Li, Xiaojing Xu, Zhuan Ye. On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1535-1568. doi: 10.3934/dcds.2021163

2020 Impact Factor: 1.916


  • PDF downloads (57)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]