American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 747-753. doi: 10.3934/proc.2011.2011.747

Power-law approximation of Bean's critical-state model with displacement current

Frank Jochmann 1,

1. 

Technische Universität Berlin, Fakultät II - Mathematik und Naturwissenschaften, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin

Received  July 2010 Revised  January 2011 Published  October 2011

The paper deals with Bean's critical state model for the description of the electromagnetic field in type-II superconductors in the case where the displacement current is not neglected at least in the surrounding insulating medium. The main goal is the approximation of the Voltage-current relation in the critical state model by a power law.
Keywords: Bean's critical state model, approximation, initial-boundary-value problem, Maxwell's equations.
Mathematics Subject Classification: Primary: 35Q60, 35D05; Secondary: , 58E35.
Citation: Frank Jochmann. Power-law approximation of Bean's critical-state model with displacement current. Conference Publications, 2011, 2011 (Special) : 747-753. doi: 10.3934/proc.2011.2011.747
[1]

Goro Akagi. Doubly nonlinear evolution equations and Bean's critical-state model for type-II superconductivity. Conference Publications, 2005, 2005 (Special) : 30-39. doi: 10.3934/proc.2005.2005.30
[2]

Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initial-boundary value problem. Conference Publications, 2007, 2007 (Special) : 212-220. doi: 10.3934/proc.2007.2007.212
[3]

H. M. Yin, Ben Q. Li, Jun Zou. A degenerate evolution system modeling bean's critical-state type-II superconductors. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 781-794. doi: 10.3934/dcds.2002.8.781
[4]

Ivonne Rivas, Muhammad Usman, Bing-Yu Zhang. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control & Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61
[5]

Björn Birnir, Niklas Wellander. Homogenized Maxwell's equations; A model for ceramic varistors. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 257-272. doi: 10.3934/dcdsb.2006.6.257
[6]

Peng Jiang. Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 3015-3037. doi: 10.3934/dcds.2015.35.3015
[7]

M. Eller. On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 473-481. doi: 10.3934/dcdss.2009.2.473
[8]

Khalid Latrach, Hatem Megdiche. Time asymptotic behaviour for Rotenberg's model with Maxwell boundary conditions. Discrete & Continuous Dynamical Systems, 2011, 29 (1) : 305-321. doi: 10.3934/dcds.2011.29.305
[9]

Cleverson R. da Luz, Gustavo Alberto Perla Menzala. Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 547-558. doi: 10.3934/dcdss.2009.2.547
[10]

Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545
[11]

Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117
[12]

Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems & Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159
[13]

Ning-An Lai, Yi Zhou. Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1499-1510. doi: 10.3934/cpaa.2018072
[14]

W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 431-444. doi: 10.3934/cpaa.2005.4.431
[15]

S. S. Krigman. Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain. Conference Publications, 2007, 2007 (Special) : 590-601. doi: 10.3934/proc.2007.2007.590
[16]

Dirk Pauly. On Maxwell's and Poincaré's constants. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 607-618. doi: 10.3934/dcdss.2015.8.607
[17]

Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 431-444. doi: 10.3934/dcds.1998.4.431
[18]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056
[19]

Shao-Yuan Huang, Shin-Hwa Wang. On S-shaped bifurcation curves for a two-point boundary value problem arising in a theory of thermal explosion. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 4839-4858. doi: 10.3934/dcds.2015.35.4839
[20]

Hideo Ikeda, Koji Kondo, Hisashi Okamoto, Shoji Yotsutani. On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows. Communications on Pure & Applied Analysis, 2003, 2 (3) : 381-390. doi: 10.3934/cpaa.2003.2.381

 Impact Factor: 

Tools

Metrics

  • PDF downloads (95)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences