Asymptotics for the time-dependent thermistor problem
Author:
Giovanni Cimatti
Journal:
Quart. Appl. Math. 62 (2004), 471-476
MSC:
Primary 35K55; Secondary 34C25, 35B35, 35B40
DOI:
https://doi.org/10.1090/qam/2086040
MathSciNet review:
MR2086040
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Abstract: Using the Liapunoff method, the global asymptotic stability of the stationary solution of the time-dependent thermistor problem is proved.
- Walter Allegretto, Yanping Lin, and Shuqing Ma, Existence and long time behaviour of solutions to obstacle thermistor equations, Discrete Contin. Dyn. Syst. 8 (2002), no. 3, 757–780. MR 1897880, DOI https://doi.org/10.3934/dcds.2002.8.757
- W. Allegretto and H. Xie, A non-local thermistor problem, European J. Appl. Math. 6 (1995), no. 1, 83–94. MR 1317875, DOI https://doi.org/10.1017/S0956792500001686
- S. N. Antontsev and M. Chipot, The thermistor problem: existence, smoothness uniqueness, blowup, SIAM J. Math. Anal. 25 (1994), no. 4, 1128–1156. MR 1278895, DOI https://doi.org/10.1137/S0036141092233482
- Giovanni Cimatti, On the stability of the solution of the thermistor problem, Appl. Anal. 73 (1999), no. 3-4, 407–423. MR 1745972, DOI https://doi.org/10.1080/00036819908840788
Hyde, F. J., Thermistors, Iliffe Books (1971), London.
- Sam Howison, A note on the thermistor problem in two space dimensions, Quart. Appl. Math. 47 (1989), no. 3, 509–512. MR 1012273, DOI https://doi.org/10.1090/qam/1012273
- S. D. Howison, J. F. Rodrigues, and M. Shillor, Stationary solutions to the thermistor problem, J. Math. Anal. Appl. 174 (1993), no. 2, 573–588. MR 1215637, DOI https://doi.org/10.1006/jmaa.1993.1142
- A. A. Lacey, Thermal runaway in a non-local problem modelling Ohmic heating. I. Model derivation and some special cases, European J. Appl. Math. 6 (1995), no. 2, 127–144. MR 1331495, DOI https://doi.org/10.1017/S095679250000173X
- A. 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 (1995), no. 3, 201–224. MR 1336425, DOI https://doi.org/10.1017/S0956792500001807
Allegretto, W., Lin, Y., and Ma, S., Existence and long time behaviour of solutions to obstacle thermistor equations, Discrete and Continuous Dynamical Systems, 8 (2002), 757-780.
Allegretto, W., and Xie, H., A non-local thermistor problem, European J. of Appl. Math., 6, (1995), 83-94.
Antontsev, S. N., and Chipot, M., The thermistor problem: existence, smoothness, uniqueness and blow up, SIAM J. Math. Anal., 25 (1994), 209-223.
Cimatti, G., On the stability of the solution of the thermistor problem, Appl. Anal., 73 (1999), 407-423.
Hyde, F. J., Thermistors, Iliffe Books (1971), London.
Howison, S. D., A note on the thermistor problem in two space dimensions, Quart. Appl. Math., 98 (1989), 37-39.
Howison, S. D., Rodrigues, J. F., and Shilor, M., Stationary solutions to the thermistor problem, J. Math. Anal. Appl. 174 (1993), 573-588.
Lacey, A., Thermal runaway in a nonlocal problem modelling Ohmic heating: Part I: Model derivation and some special cases, Euro Jnl. Appl. Math, 6 (1995), 127-144.
Lacey, A., Thermal runaway in a nonlocal problem modelling Ohmic heating: Part II: General proof of blow-up and asymptotic of runaway, Euro Jnl. Appl. Math, 6 (1995), 201-224.
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© Copyright 2004
American Mathematical Society