July  2009, 25(2): 545-565. doi: 10.3934/dcds.2009.25.545

A variational inequality in Bean's model for superconductors with displacement current

1. 

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

Received  September 2008 Revised  January 2009 Published  June 2009

The paper deals with Bean's critical state model for the description of the electromagnetic field in superconductors. A variational inequality for the quasi-stationary approximation on a part of the spatial domain is given. The main goals are the existence, uniqueness and asymptotic behavior as $t\rightarrow\infty$ of the solutions to that system.
Citation: Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545
[1]

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 and Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61

[2]

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

[3]

Dina Kalinichenko, Volker Reitmann, Sergey Skopinov. Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion. Conference Publications, 2013, 2013 (special) : 407-414. doi: 10.3934/proc.2013.2013.407

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

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

[10]

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

[11]

Byung-Hoon Hwang, Seok-Bae Yun. Stationary solutions to the boundary value problem for the relativistic BGK model in a slab. Kinetic and Related Models, 2019, 12 (4) : 749-764. doi: 10.3934/krm.2019029

[12]

Yuri Kalinin, Volker Reitmann, Nayil Yumaguzin. Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect. Conference Publications, 2011, 2011 (Special) : 754-762. doi: 10.3934/proc.2011.2011.754

[13]

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

[14]

Fritz Colonius. Invariance entropy, quasi-stationary measures and control sets. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 2093-2123. doi: 10.3934/dcds.2018086

[15]

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

[16]

Annalena Albicker, Roland Griesmaier. Monotonicity in inverse scattering for Maxwell's equations. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022032

[17]

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

[18]

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

[19]

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

[20]

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

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (57)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]