Numerical solutions of the thermistor equations

Journal of Computational and Applied Mathematics

Volumn 79, Issue 1, 1997, Pages 101-118

  Zhou, S ^a   Westbrook, D R ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Heat conduction; Thermistor

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; HEAT CONDUCTION; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

ONE DIMENSIONAL NONLOCAL PARABOLIC INITIAL BOUNDARY VALUE PROBLEMS; STEADY STATE PROBLEMS; TRANSIENT PROBLEMS;

THERMISTORS;

EID: 0031550739     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00166-5     Document Type: Article

References (15)

1. W. Allegretto and H. Xie, Existence of solutions for the time dependent thermistor equation, IMA. J. Appl. Math. 48 (1992) 271-281.
2. G. Cimatti, A bound for temperature in thermistor problem, IMA J. Appl. Math. 40 (1988) 15-22.
3. G. Cimatti, Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Quart. Appl. Math. 47 (1989) 117-121.
4. G. Cimatti, The stationary thermistor with a current limiting device, Proc. Roy. Soc. Edinburgh A 116 (1990) 79-84.
5. G. Cimatti and G. Prodi, Existence results for a nonlinear ellieeptic system modelling a temperature dependent electrical resistor, Ann. Mat. Pure Appl. 152 (1988) 227-236.
6. X. Chen, Existence and regularity of solutions of a nonlinear degenerate elliptic system arising from a thermistor problem, private communication (1991).
7. X. Chen and A. Friedman, The thermistor problem with one-zero conductivity, IMA preprint series # 793, 1991.
8. H. Diesselhorst, Uber das Probleme eines Electrisch Erwarmter Leiter, Ann. Phys. 1 (1900) 312-325.
9. A.C. Fowler, I. Frigaard and S.D. Howison, Temperature surges in current-limiting circuit devices, SIAM Appl. Math. 52 (1992) 998-1011.
10. S.D. Howison, Complex variables in industrial mathematics, in: N. Neunzert, ed. Proc. 2nd European Sympos. on Mathematics in Industry, Oberwolfach, Germany (Teubner, Stuttguart, Germany, 1988) 153-166.
11. H.B. Keller, Numerical Solutions of Two Point Boundary Value Problems (SIAM, Philadelphia, 1976).
12. D.R. Westbrook, The thermistor, a problem in heat and current flow, Numer. Methods in Partial Differential Equations, Vol. 5 (1989) 259-273.
13. H. Xie and W. Allegretto, Cα(Ω) solutions of a class of nonlinear degenerate elliptic systems arising in the thermistor problem, SIAM J. Math. Anal 22 (1991) 1491-1499.
14. S. Zhou, Existence, uniqueness and numerical realization of solutions for the thermistor equation, PhD Thesis, University of Calgary, 1993.
15. S. Zhou and D.R. Westbrook, Solution of the thermistor equation, University of Calgary, Department of Mathematics, Preprint series 761, 1994.