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Analysis of blowup for the thermistor problem

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References

  1. S. N. Antontsev and M. Chipot, “The thermistor problem: existence, smoothness, uniqueness, blowup,” SIAM J. Math. Anal.,25, No. 4, 1128–1156 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. N. Antontsev and M. Chipot, “Some results on the thermistor problem,” in: Proceedings of the Conference ‘Free-Boundary Problems in Continuum Mechanics’” (Novosibirsk, 1991), Intern. Ser. Numer. Math., Birkhäuser, Basel, 1992,106, pp. 47–57.

    Google Scholar 

  3. S. N. Antontsev and M. Chipot, “Existence, stability and blowup of the solution for the thermistor problem,” Dokl. Akad. Nauk,324, No. 2, 309–313 (1992).

    MathSciNet  Google Scholar 

  4. S. N. Antontsev and M. Chipot, “Analysis of blowup for the thermistor problem,” in: Abstracts: The International Conference ‘Advanced Mathematics, Computations and Applications (AMCA-95)’” (Novosibirsk, June 20–24), Novosibirsk, 1995.

  5. G. Cimatti, Existence of Weak Solutions for the Nonstationary Problem of the Joule Heating of a Conductor [Preprint/Università di Pisa] (to appear).

  6. G. Cimatti, “A bound for the temperature in the thermistor problem,” J. Appl. Math. Mech.,40, No. 1, 15–22 (1988).

    MATH  MathSciNet  Google Scholar 

  7. G. Cimatti, “Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions,” Quart. Appl. Math.,47, No. 1, 117–121 (1989).

    MATH  MathSciNet  Google Scholar 

  8. M. Chipot, J. I. Diaz, and R. Kersner, “Existence and uniqueness results for the thermistor problem with temperature dependent conductivity” (to appear).

  9. S. D. Howison, J. F. Rodrigues, and M. Shillor, “Stationary solutions to the thermistor problem,” J. Math. Anal. Appl.,174, No. 2, 573–588 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  10. X. Xu, A Stefan Like Problem Arising from the Electrical Heating of a Conductor with Conductivity Vanishing at Finite Temperature [Preprint] (to appear).

  11. A. Lacey, “Thermal runaway in a non-local problem modelling Ohmic heating. II. General proof of blow-up and asymptotics of runaway,” European J. Appl. Math.,6, No. 3, 201–224 (1995).

    MATH  MathSciNet  Google Scholar 

  12. M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Inc., Englewood Cliffs, New York (1967).

    Google Scholar 

  13. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, Berlin (1985).

    Google Scholar 

  14. A. Lacey, “Thermal runaway in a non-local problem modelling Ohmic heating. I. Model derivation and some special cases,” European J. Appl. Math.,6, No. 2, 127–144 (1995).

    Article  MATH  MathSciNet  Google Scholar 

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This article was partly sponsored by a grant of INTAS.

Novosibirsk, Zürich. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 5, pp. 963–977, September–October, 1997.

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Antontsev, S.N., Chipot, M. Analysis of blowup for the thermistor problem. Sib Math J 38, 827–841 (1997). https://doi.org/10.1007/BF02673024

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