A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor

Xinfu Chen; Avner Friedman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1992)

  • Volume: 19, Issue: 4, page 615-636
  • ISSN: 0391-173X

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Xinfu Chen, and 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 19.4 (1992): 615-636. <http://eudml.org/doc/84139>.

@article{XinfuChen1992,
author = {Xinfu Chen, Friedman, Avner},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {electric circuit breaker; unique solvability; conformal mapping; variational inequality},
language = {eng},
number = {4},
pages = {615-636},
publisher = {Scuola normale superiore},
title = {A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor},
url = {http://eudml.org/doc/84139},
volume = {19},
year = {1992},
}

TY - JOUR
AU - Xinfu Chen
AU - Friedman, Avner
TI - A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1992
PB - Scuola normale superiore
VL - 19
IS - 4
SP - 615
EP - 636
LA - eng
KW - electric circuit breaker; unique solvability; conformal mapping; variational inequality
UR - http://eudml.org/doc/84139
ER -

References

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  1. [1] H. Behenke - F. Sommer, Theorie der Analytischen Funktionen einer Komplexen Veränderlichen, Springer-Verlag, New York, 1976. Zbl0324.30001
  2. [2] X. Chen - A. Friedman, The thermistor problem for conductivity which vanishes at large temperature, Quart. Appl. Math., to appear. Zbl0803.35051MR1205940
  3. [3] G. Cimatti, A bound for the temperature in the thermistor problem, IMA J. Appl. Math., 40 (1988), 15-22. Zbl0694.35139MR983747
  4. [4] G. Cimatti, Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Quart. Appl. Math.47 (1989), 117-121. Zbl0694.35137MR987900
  5. [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. Zbl0675.35039MR980982
  6. [6] A. Friedman, Variational Principles and Free Boundary Problems, Wiley-InterScience, New-York, (1982). Zbl0564.49002MR679313
  7. [7] S.D. Howson, A note on the thermistor problem in two space dimensions, Quart. Appl. Math., 47 (1989), 509-512. Zbl0692.35094MR1012273
  8. [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. Zbl0709.00507MR1128117
  9. [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. [10] F.J. Hyde, Thermistors, Iliffe Books, London, 1971. 
  11. [11] J.F. Llewellyn, The Physics of Electrical Contacts, Oxford, Clarendon Press, 1957. 
  12. [12] D.R. Westbrook, The thermistor: a problem in heat and current flow, Numeric. Methods Partial Differential Equations, 5 (1989), 259-273. Zbl0676.65128MR1107888
  13. [13] J.M. Young, Steady state Joule heating with temperature dependent conductivities, Appl. Sci. Res., 43 (1986), 55-65. Zbl0616.76101

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