Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium

A. Bermúdez; M. C. Muniz; P. Quintela

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 4, page 399-430
  • ISSN: 0294-1449

How to cite

top

Bermúdez, A., Muniz, M. C., and Quintela, P.. "Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium." Annales de l'I.H.P. Analyse non linéaire 15.4 (1998): 399-430. <http://eudml.org/doc/78442>.

@article{Bermúdez1998,
author = {Bermúdez, A., Muniz, M. C., Quintela, P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {piecewise homogeneous media; thermal modelling of aluminium electrolytic cells; weak formulation},
language = {eng},
number = {4},
pages = {399-430},
publisher = {Gauthier-Villars},
title = {Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium},
url = {http://eudml.org/doc/78442},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Bermúdez, A.
AU - Muniz, M. C.
AU - Quintela, P.
TI - Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 4
SP - 399
EP - 430
LA - eng
KW - piecewise homogeneous media; thermal modelling of aluminium electrolytic cells; weak formulation
UR - http://eudml.org/doc/78442
ER -

References

top
  1. [1] Y. Arita, N. Urata and H. Ikeuchi, Estimation of Frozen Bath Shape in an Aluminium Reduction Cell by Computer Simulation, Light Metals, 1978, pp. 59-72. 
  2. [2] G. Bayada and M. Chambat, Existence and Uniqueness for a Lubrication Problem with Nonregular Conditions on the Free Boundary, Boll. U.M.I., Vol. 3–B 6, 1984, pp. 543-557. Zbl0612.35026MR762718
  3. [3] A. Bermúdez, L. Carpintero, M.C. MUÑIZ and P. Quintela, An Inverse Problem Related to the Three-dimensional Modelling of Aluminium Electrolytic Cells. In L. C. Wrobel and C. A. Brebbia, editors, Computational Modelling of Free and Moving Boundary Problems II, Computational Mechanics Publications, 1993, pp. 377-388. 
  4. [4] A. Bermúdez, M.C. MUÑIZ and P. Quintela, Numerical Solution of a Three-dimensional Thermoelectric Problem Taking Place in an Aluminium Electrolytic Cell, Computer Methods in Applied Mechanics and Engineering, Vol. 106, 1993, pp. 129-142. Zbl0800.76240MR1229188
  5. [5] A. Bermúdez, M.C. MUÑIZ and P. Quintela, Numerical Solution of a Stefan Problem Arising in the Thermoelectrical Modelling of Aluminium Electrolytic Cells. In L. C. Wrobel and C. A. Brebbia, editors, Computational Modelling of Free and Moving Boundary Problems, Vol. 2, Computational Mechanics Publications/De Gruyter, 1991, pp. 39-58. Zbl0838.35142MR1162758
  6. [6] A. Bermúdez, M.C. MUÑIZ and P. Quintela, Existence and Uniqueness for a Free Boundary Problem in Aluminium Electrolysis, Journal of Mathematical Analysis and Applications, Vol. 191, 1995, pp. 497-527. Zbl0821.35155MR1325815
  7. [7] H. Brezis, Analyse Fonctionnelle. Théorie et Applications, Masson, Paris, 1983. Zbl0511.46001MR697382
  8. [8] H. Brezis, D. Kinderlehrer and G. Stampacchia, Sur une Nouvelle Formulation du Problème de L'écoulement à Travers une Digue, C. R. Acad. Sc. Paris, Vol. A 287, 1978, pp. 711-714. Zbl0391.76072MR515672
  9. [9] J. Carrillo-Menéndez and M. Chipot, On the Dam Problem, Journal of Differential Equations, Vol. 45, 1982, pp. 234-271. Zbl0504.35082MR665999
  10. [10] J. Durany and C. Vázquez, Numerical Approach of Lubrication Problems in Journal Bearing Devices with Axial Supply. In Ch. Hirsch et al., editors, Numerical Methods in Engineering '92, Elsevier Science Publishers B.V., 1992, pp. 839-844. 
  11. [11] K. Grjotheim, C. Krohn, M. Malinovsky, K. Matiašovsky and J. Thonstad, Aluminium Electrolysis, Aluminium Verlag, Dusseldorf, 1982. 
  12. [12] K. Grjotheim and H. Kvande, Understanding the Hall-Héroult Process for Production of Aluminium, Aluminium Verlag, Dusseldorf, 1986. 
  13. [ 13] S.D. Howison, J.F. Rodrigues and M. Shillor, Stationary Solutions to the Thermistor Problem, J. Math. Anal. Appl., Vol. 174, 1993, pp. 573-588. Zbl0787.35033MR1215637
  14. [14] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, 1980. Zbl0457.35001MR567696
  15. [15] M.C. MUÑIZ, Estudio Matemático de un Problema de Stefan Relacionado con la Modelización Termoeléctrica de Cubas de Electrolisis de Aluminio, PhD thesis, Universidad de Santiago de Compostela, 1995. 
  16. [16] T. ROUBíČEK, The Stefan Problem in Heterogeneous Media, Ann. Inst. Henri Poincaré, Vol. 6(6), 1989, pp. 481-501. Zbl0706.35139MR1035339
  17. [17] C. Saguez, Un Problème de Stefan avec Source sur la Frontière Libre, Rapport de Recherche INRIA n. 268, Rocquencourt, 1977. 
  18. [18] M.P. Taylor and B.J. Welch, Melt/freeze Heat Transfer Measurements in Cryolite-based Electrolytes, Metallurgical Trans., Vol. B. 18, 1987, pp. 391-398. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.