A parabolic quasi-variational inequality arising in a superconductivity model
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 1, p. 153-169
@article{ASNSP_2000_4_29_1_153_0,
     author = {Rodrigues, Jos\'e Francisco and Santos, Lisa},
     title = {A parabolic quasi-variational inequality arising in a superconductivity model},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {1},
     year = {2000},
     pages = {153-169},
     zbl = {0953.35079},
     mrnumber = {1765540},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_1_153_0}
}
Rodrigues, José Francisco; Santos, Lisa. A parabolic quasi-variational inequality arising in a superconductivity model. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 1, pp. 153-169. http://www.numdam.org/item/ASNSP_2000_4_29_1_153_0/

[1] C. Baiocchi - A. Capelo, "Variational and Quasivariational Inequalities. Applications to Free Boundary Problems", J. Wiley & Sons, Chischester-New York, 1984. | MR 745619 | Zbl 0551.49007

[2] A. Bensoussan - J.L. Lions, "Contrôle impulsionel et inéquations quasivariationelles", Dunod, Paris, 1982. | Zbl 0491.93002

[3] E.H. Brandt, Electric field in superconductors with regular cross-sections, Phys. Rev. B 52 (1995), 15442-15457.

[4] E. Dibenedetto, "Degenerate Parabolic Equations", Springer-Verlag, New York, 1993. | MR 1230384 | Zbl 0794.35090

[5] C. Gerhardt, On the existence and uniqueness of a warpeningfunction in the elastic-plastic torsion of a cylindrical bar with multiply connected cross-section, A. Dold - B. Eckmann - P. Germain - B. Nayroles (eds.), Lecture Notes in Math. 503, Springer, Berlin, 1976. | MR 669229 | Zbl 0354.73034

[6] Y.B. Kim - C.F. Hempstead - A.R. Strnad, Critical persistent currents in hard superconductors, Phys. Rev. Lett. 9 (1962), 306-309.

[7] M.M. Kunze - M.D.P. Monteiro Marques, A note on Lipschitz continuous solutions of a parabolic quasi-variational inequality, In "Nonlinear Evolutionary Equations and their Applications", T. T. Li - L. W. Lin - J. F. Rodrigues (eds.), World Scientific, Singapore, 1999, pp. 109-115. | MR 1734576 | Zbl 0972.47058

[8] M.M. Kunze - J.F. Rodrigues, An elliptic quasi-variational inequality with gradient constants and some of its applications, Math. Methods. Appl. Sci., to appear. | MR 1765905 | Zbl 0956.35059

[9] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'Ceva, "Linear and quasilinear equations of parabolic type", Translations of Mathematical Monographs 23, AMS, 1968. | MR 241822 | Zbl 0174.15403

[10] L. Prighozin, Variational model of sandpile growth, European J. Appl. Math. 7 (1996), 225-235. | MR 1401168 | Zbl 0913.73079

[11] L. Prighozin, On the Bean critical state model in superconductivity, European J. Appl. Math. 7 (1996), 237-247. | MR 1401169 | Zbl 0873.49007

[12] L. Santos, A diffusion problem with gradient constraint and evolutive Dirichlet condition, Portugaliae Mathematica 48 (1991), 441-468. | MR 1147610 | Zbl 0773.49006

[13] J. Simon, Compact sets in the space Lp(0, T ; B), Ann. Mat. Pura Appl. 146 (1987), 65-96. | MR 916688 | Zbl 0629.46031