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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

Error estimates for the Chernoff scheme to approximate a nonlocal parabolic problem; 359-372

Full article in PDF format | 10.3176/phys.math.2007.4.07

Moulay Rchid Sidi Ammi, Olena Mul


We study a nonlocal parabolic equation obtained from the reduction of the well-known thermistor problem. Error estimate bounds are established for a family of time discretization scheme originated by E. Magenes in Analyse Mathématique et Applications (Gauthier–Villars, Paris, 1988).


1. Cimatti, G. A remark on the thermistor problem with rapidly growing conductivity. Appl. Anal., 2001, 1–2, 133–140.

2. Antontsev, S. N. and Chipot, M. The thermistor problem: existence, smoothness uniqueness, blowup. SIAM J. Math. Anal., 1994, 4, 1128–1156.

3. Chipot, M. and Cimatti, G. A uniqueness result for the thermistor problem. European J. Appl. Math., 1991, 2, 97–103.

4. Allegretto, A., Yanping Lin and Shunqing Ma. On the time periodic thermistor problem. European J. Appl. Math., 2004, 15, 55–77.

5. El Hachimi, A. and Sidi Ammi, M. R. Existence of global solution for a nonlocal parabolic problem. Electron. J. Qual. Theory Differ. Equations, 2005, 1, 1–9.

6. El Hachimi, A. and Sidi Ammi, M. R. Semi-discretization for a nonlocal parabolic problem. Int. J. Math. Math. Sci., 2005, 10, 1655–1664.

7. Hyung-Chun Lee and Timofey Shi Lkin. Analysis of optimal control problems for the two-dimensional thermistor system. Siam. J. Control. Optimal, 2005, 1, 268–282.

8. Lacey, A. A. Thermal runway in a non-local problem modelling ohmic heating, part I: model derivation and some special cases. European J. Appl. Math., 1995, 6, 127–144.

9. Lacey, A. A. Thermal runway in a non-local problem modelling ohmic heating, part II: general proof of blow-up and asymptotics runways. European J. Appl. Math., 1995, 6, 201–224.

10. Magenes, E. Remarques sur l’approximation des problèmes paraboliques non linéaires. In Analyse Mathématique et Applications. Gauthier–Villars, Paris, 1988, 1–21.

11. Massera, A. Optimisation et simulation numérique du chauffage par induction pour le procédé de thixoformage. Thèse soutenue à L’École Polytechnique Féderale de Lausane, 2003.

12. Verdi, C. and Visintin, A. Error estimates for a semi-explicit numerical scheme for stefantype problem. Numer. Math., 1988, 52, 165–195.

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