A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors

Archive for Rational Mechanics and Analysis

Volumn 192, Issue 1, 2009, Pages 87-115

  Crasta, Graziano ^a   Malusa, Annalisa ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60349096955     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0125-5     Document Type: Article

References (25)

1. A. Badía C. López 2001 Vector magnetic physteresis of hard superconductors Phys. Rev. B 65 104514
2. Badía, A., López, C.: Horizons in superconductivity research. Minimal Model for the Topology of the Critical State in Hard Superconductors. Nova Science Publishers, 2003
3. A. Badía C. López 2004 Electric field in hard superconductors with arbitrary cross section and general critical current law J. Appl. Phys. 95 8035 8040
4. Bardi, M., Capuzzo Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems and Control: Foundations and Applications. Birkhäuser, Boston, 1997
5. J.W. Barrett L. Prigozhin 2000 Bean's critical-state model as the p → ∞ limit of an evolutionary p-Laplacian equation Nonlinear Anal. 42 977 993
6. Barrett, J.W., Prigozhin, L.: Sandpiles and superconductors: dual variational formulations for critical-state problems. Systems, Control, Modeling and Optimization, IFIP Int. Fed. Inf. Process., Vol. 202. Springer, New York, 25-29, 2006
7. C.P. Bean 1962 Magnetization of hard superconductors Phys. Rev. Lett. 8 250 253
8. K.V. Bhagwat D. Karmakar G. Ravikumar 2003 Critical state model with anisotropic critical current density J. Phys. Condens. Matter 15 1325 1337
9. Braides A.: Γ-Convergence for Beginners. Oxford University Press, New York (2002)
10. E.H. Brandt 1995 Electric field in superconductors with rectangular cross section Phys. Rev. B. 52 15442 15457
11. Buttazzo, G.: Semicontinuity, relaxation and integral representation in the calculus of variations. Pitman Res. Notes Math. Ser., Vol. 207. Longman Scientific and Technical, Harlow, 1989
12. Cannarsa, P., Sinestrari, C.: Semiconcave functions, Hamilton-Jacobi equations and optimal control. Progress in Nonlinear Differential Equations and their Applications, Vol. 58. Birkhäuser, Boston, 2004
13. S.J. Chapman 2000 A hierarchy of models for type-II superconductors SIAM Rev. 42 555 598
14. G. Crasta A. Malusa 2007 The distance function from the boundary in a Minkowski space Trans Am. Math. Soc. 359 5725 5759
15. G. Crasta A. Malusa 2007 On a system of partial differential equations of Monge-Kantorovich type J. Diff. Equ. 235 484 509
16. Dal Maso G.: An Introduction to Γ-Convergence. Birkhäuser, Boston (1993)
17. Fisher, L.M., Yampol'skii, V.A.: Comment on "Critical statetheory for non-parallel flux line lattices in type-II superconductors". oai:arXiv:cond-mat/0201286, 2002
18. A. Garroni V. Nesi M. Ponsiglione 2001 Dielectric breakdown: optimal bounds Proc. R. Soc. Lond. A 457 2317 2335
19. Goldberg S.I: Curvature and Homology. Academic Press, New York (1970)
20. Y.Y. Li L. Nirenberg 2005 The distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations Commun. Pure Appl. Math. 58 85 146
21. Lions P.L.: Generalized Solutions of Hamilton-Jacobi Equations. Pitman, Boston (1982)
22. Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
23. Schneider R.: Convex Bodies: the Brunn-Minkowski Theory. Cambridge University Press, Cambridge (1993)
24. W. von Wahl 1992 Estimating u by div u and curl u Math. Methods Appl. Sci. 15 123 143
25. H.-M. Yin B.Q. Li J. Zou 2002 A degenerate evolution system modeling Bean's critical-state type-II superconductors Discrete Contin. Dyn. Syst. 8 781 794