EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 40 / No 2 (March-April 2006) ESAIM: M2AN, 40 2 (2006) 353-366 References
Free Access
Issue
ESAIM: M2AN
Volume 40, Number 2, March-April 2006
Page(s) 353 - 366
DOI https://doi.org/10.1051/m2an:2006016
Published online 21 June 2006
  1. W. Allegretto and H. Xie, A non-local thermistor problem. Eur. J. Appl. Math. 6 (1995) 83–94. [Google Scholar]
  2. W. Allegreto, Y. Lin and A. Zhou, A box scheme for coupled systems resulting from microsensor thermistor problems. Dynam. Contin. Discret. S. 5 (1999) 209–223. [Google Scholar]
  3. W. Allegreto, Y. Lin and S. Ma, Existence and long time behaviour of solutions to obstacle thermistor equations. Discrete Contin. Dyn. S. 8 (2002) 757–780. [CrossRef] [Google Scholar]
  4. S.N. Antontsev and M. Chipot, The thermistor problem: existence, smoothness, uniqueness, blowup. SIAM J. Math. Anal. 25 (1994) 1128–1156. [CrossRef] [MathSciNet] [Google Scholar]
  5. A.R. Bahadir, Application of cubic B-spline finite element technique to the thermistor problem. Appl. Math. Comput. 149 (2004) 379–387. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bermúdez, M.C. Muñiz and P. Quintela, Numerical solution of a three-dimensional thermoelectric problem taking place in an aluminum electrolytic cell. Comput. Method Appl. M. 106 (1993) 129–142. [CrossRef] [Google Scholar]
  7. O. Chau, J.R. Fernández, W. Han and M. Sofonea, A frictionless contact problem for elastic-viscoplastic materials with normal compliance and damage. Comput. Method Appl. M. 191 (2002) 5007–5026. [CrossRef] [Google Scholar]
  8. X. Chen, Existence and regularity of solutions of a nonlinear degenerate elliptic system arising from a thermistor problem. J. Partial Differential Equations 7 (1994) 19–34. [MathSciNet] [Google Scholar]
  9. P.G. Ciarlet, The finite element method for elliptic problems, in Handbook of Numerical Analysis, Vol. II, Part 1, P.G. Ciarlet and J.L. Lions Eds., North Holland (1991) 17–352. [Google Scholar]
  10. G. Cimatti, Remark on the existence and uniqueness for the thermistor problem under mixed boundary conditions. Quart. J. Mech. Appl. Math. 47 (1989) 117–121. [Google Scholar]
  11. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics, Springer, New-York (1976). [Google Scholar]
  12. J.R. Fernández, K.L. Kuttler, M.C. Muñiz and M. Shillor, A model and simulations of the thermoviscoelastic thermistor. Eur. J. Appl. Math. (submitted). [Google Scholar]
  13. W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity, Americal Mathematical Society–International Press (2002). [Google Scholar]
  14. S.D. Howison, A note on the thermistor problem in two space dimension. Quart. J. Mech. Appl. Math. 47 (1989) 509–512. [Google Scholar]
  15. S.D. Howison, J. Rodrigues and M. Shillor, Stationary solutions to the thermistor problem. J. Math. Anal. Appl. 174 (1993) 573–588. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Kutluay, A.R. Bahadir and A. Ozdeć, A variety of finite difference methods to the thermistor with a new modified electrical conductivity. Appl. Math. Comput. 106 (1999) 205–213. [CrossRef] [MathSciNet] [Google Scholar]
  17. S. Kutluay, A.R. Bahadir and A. Ozdeć, Various methods to the thermistor problem with a bulk electrical conductivity. Int. J. Numer. Method. Engrg. 45 (1999) 1–12. [CrossRef] [Google Scholar]
  18. S. Kutluay and E. Esen, A B-spline finite element method for the thermistor problem with the modified electrical conductivity. Appl. Math. Comput. 156 (2004) 621–632. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Kutluay and A.S. Wood, Numerical solutions of the thermistor problem with a ramp electrical conductivity. Appl. Math. Comput. 148 (2004) 145–162. [CrossRef] [MathSciNet] [Google Scholar]
  20. K.L. Kuttler, M. Shillor and J.R. Fernández, Existence for the thermoviscoelastic thermistor problem. Differential Equations Dynam. Systems (to appear). [Google Scholar]
  21. H. Xie and W. Allegretto, Formula solutions of a class of nonlinear degenerate elliptic systems arising in the thermistor problem. SIAM J. Math. Anal. 22 (1991) 1491–1499. [CrossRef] [MathSciNet] [Google Scholar]
  22. X. Xu, The thermistor problem with conductivity vanishing for large temperature. P. Roy. Soc. Edinb. A 124 (1994) 1–21. [Google Scholar]
  23. X. Xu, On the existence of bounded temperature in the thermistor problem with degeneracy. Nonlinear Anal. 42 (2000) 199–213. [CrossRef] [MathSciNet] [Google Scholar]
  24. X. Xu, On the effects of thermal degeneracy in the thermistor problem. SIAM J. Math. Anal. 35 (4) (2003) 1081–1098. [Google Scholar]
  25. X. Xu, Local regularity theorems for the stationary thermistor problem. P. Roy. Soc. Edinb. A 134 (2004) 773–782. [CrossRef] [Google Scholar]
  26. S. Zhou and D.R. Westbrook, Numerical solutions of the thermistor equations. J. Comput. Appl. Math. 79 (1997) 101–118. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you