×

zbMATH — the first resource for mathematics

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).

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B60 Continuation and prolongation of solutions to PDEs
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.