A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 19 (1992) no. 4, p. 615-636 
@article{ASNSP_1992_4_19_4_615_0,
     author = {Xinfu Chen and Friedman, Avner},
     title = {A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {4},
     year = {1992},
     pages = {615-636},
     zbl = {0780.35116},
     mrnumber = {1205886},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1992_4_19_4_615_0}
}

Xinfu Chen; Friedman, Avner. A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 19 (1992) no. 4, pp. 615-636. http://www.numdam.org/item/ASNSP_1992_4_19_4_615_0/

[1] H. Behenke - F. Sommer, Theorie der Analytischen Funktionen einer Komplexen Veränderlichen, Springer-Verlag, New York, 1976. | Zbl 0324.30001

[2] X. Chen - A. Friedman, The thermistor problem for conductivity which vanishes at large temperature, Quart. Appl. Math., to appear. | MR 1205940 | Zbl 0803.35051

[3] G. Cimatti, A bound for the temperature in the thermistor problem, IMA J. Appl. Math., 40 (1988), 15-22. | MR 983747 | Zbl 0694.35139

[4] G. Cimatti, Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Quart. Appl. Math. 47 (1989), 117-121. | MR 987900 | Zbl 0694.35137

[5] G. Cimatti - G. Prodi, Existence results for a nonlinear elliptic systems modelling a temperature dependent electrical resistor, Ann. Mat. Pura Appl., (4) 152 (1988), 227-236. | MR 980982 | Zbl 0675.35039

[6] A. Friedman, Variational Principles and Free Boundary Problems, Wiley-InterScience, New-York, (1982). | MR 679313 | Zbl 0564.49002

[7] S.D. Howson, A note on the thermistor problem in two space dimensions, Quart. Appl. Math., 47 (1989), 509-512. | MR 1012273 | Zbl 0692.35094

[8] S.D. Howison, Complex variables in Industrial Mathematics, Proceeding Second European Symposium on Mathematics in Industry, ESMI II, March 1-7, 1987, Oberwolfach, H. Neunzert ed., B.G. Teubner Stuttgart and Kluwer Academic Publishers, 1988, 153-166. | MR 1128117 | Zbl 0709.00507

[9] S.D. Howison - J.F. Rodrigues - M. Shillor, Existence results for the problems of Joule heating of a resistor, J. Math. Anal. Appl., to appear.

[10] F.J. Hyde, Thermistors, Iliffe Books, London, 1971.

[11] J.F. Llewellyn, The Physics of Electrical Contacts, Oxford, Clarendon Press, 1957.

[12] D.R. Westbrook, The thermistor: a problem in heat and current flow, Numeric. Methods Partial Differential Equations, 5 (1989), 259-273. | MR 1107888 | Zbl 0676.65128

[13] J.M. Young, Steady state Joule heating with temperature dependent conductivities, Appl. Sci. Res., 43 (1986), 55-65. | Zbl 0616.76101