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Antontsev, S. N.; Shipo, M.

Analytic regimes with peaking in the thermistor problem. (English. Russian original) Zbl 1042.35579

Sib. Math. J. 38, No. 5, 827-841 (1997); translation from Sib. Mat. Zh. 38, No. 5, 963-977 (1997).

Cited in 3 Documents

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B60 Continuation and prolongation of solutions to PDEs
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\textit{S. N. Antontsev} and \textit{M. Shipo}, Sib. Math. J. 38, No. 5, 963--977 (1997; Zbl 1042.35579); translation from Sib. Mat. Zh. 38, No. 5, 963--977 (1997)
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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). · Zbl 0808.35059
[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. · Zbl 0817.35114
[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). · Zbl 0817.35114
[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. · Zbl 0808.35059
[5] G. Cimatti, Existence of Weak Solutions for the Nonstationary Problem of the Joule Heating of a Conductor [Preprint/Università di Pisa] (to appear). · Zbl 0769.35059
[6] G. Cimatti, ”A bound for the temperature in the thermistor problem,” J. Appl. Math. Mech.,40, No. 1, 15–22 (1988). · Zbl 0694.35139
[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). · Zbl 0694.35137
[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). · Zbl 0787.35033
[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). · Zbl 0849.35058
[12] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Inc., Englewood Cliffs, New York (1967). · Zbl 0153.13602
[13] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, Berlin (1985). · Zbl 1042.35002
[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). · Zbl 0843.35008
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