About existence of equilibria in electromagnetic casting
Authors:
Antoine Henrot and Michel Pierre
Journal:
Quart. Appl. Math. 49 (1991), 563-575
MSC:
Primary 78A55
DOI:
https://doi.org/10.1090/qam/1121687
MathSciNet review:
MR1121687
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Additional Information
J.-P. Brancher, R. De Framond, and O. Sero-Guillaume, Shaping of liquid metal cylinders, 4th Beer Sheva Seminar on MHD Flows and Turbulence, Israel, 1984
J.-P. Brancher, J. Etay, and O. Sero-Guillaume, Formage d’une lame, J. Méc. Théor. Appl. 2 (6), 976–989 (1983)
J.-P. Brancher and O. Sero-Guillaume, Sur l’équilibre des liquides magnétiques. Application à la magnétostatique, J. Méc. Theor. Appl. 2 (2), 265–283 (1983)
- Haïm Brézis and Walter A. Strauss, Semi-linear second-order elliptic equations in $L^{1}$, J. Math. Soc. Japan 25 (1973), 565–590. MR 336050, DOI https://doi.org/10.2969/jmsj/02540565
O. Coulaud and A. Henrot, Numerical study of a free boundary problem arising in electromagnetic casting (to appear)
- Michel Crouzeix and Jean Descloux, A bidimensional electromagnetic problem, SIAM J. Math. Anal. 21 (1990), no. 3, 577–592. MR 1046790, DOI https://doi.org/10.1137/0521031
- Robert Dautray and Jacques-Louis Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. 1, INSTN: Collection Enseignement. [INSTN: Teaching Collection], Masson, Paris, 1987 (French). Modèles physiques. [Physical models]; With the collaboration of Michel Cessenat, André Gervat and Hélène Lanchon; Reprinted from the 1984 edition. MR 918560
- Antoine Henrot and Michel Pierre, Un problème inverse en formage des métaux liquides, RAIRO Modél. Math. Anal. Numér. 23 (1989), no. 1, 155–177 (French, with English summary). MR 1015924, DOI https://doi.org/10.1051/m2an/1989230101551
- A. Henrot and M. Pierre, About existence of a free boundary in electromagnetic shaping, Recent advances in nonlinear elliptic and parabolic problems (Nancy, 1988) Pitman Res. Notes Math. Ser., vol. 208, Longman Sci. Tech., Harlow, 1989, pp. 283–293. MR 1035015
- Yoshio Konishi, Semi-linear Poisson’s equations, Proc. Japan Acad. 49 (1973), 100–105. MR 331134
- Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
J. A. Shercliff, Magnetic shaping of molten metal columns, Proc. Roy. Soc. London Ser. A. 375, 455–473 (1981)
J.-P. Brancher, R. De Framond, and O. Sero-Guillaume, Shaping of liquid metal cylinders, 4th Beer Sheva Seminar on MHD Flows and Turbulence, Israel, 1984
J.-P. Brancher, J. Etay, and O. Sero-Guillaume, Formage d’une lame, J. Méc. Théor. Appl. 2 (6), 976–989 (1983)
J.-P. Brancher and O. Sero-Guillaume, Sur l’équilibre des liquides magnétiques. Application à la magnétostatique, J. Méc. Theor. Appl. 2 (2), 265–283 (1983)
H. Brezis and W. A. Strauss, Semi-linear second order elliptic equations in $L^{1}$ , J. Math. Soc. Japan 25, 565–590 (1973)
O. Coulaud and A. Henrot, Numerical study of a free boundary problem arising in electromagnetic casting (to appear)
M. Crouzeix and J. Descloux, A bidimensional electromagnetic problem, SIAM J. of Math. Anal. 21 (3), , 577–592 (1990)
R. Dautray and J.-L. Lions, Analyse mathématique et Calcul numérique pour les sciences et les techniques, Vol. 1, Masson, 1984
A. Henrot and M. Pierre, Un problème inverse en formage des métaux liquides, RAIRO Modél. Math. Anal. Numer. 23 (1), 155–177 (1989)
A. Henrot and M. Pierre, About existence of a free boundary in electromagnetic shaping, Recent Advances in Nonlinear Elliptic and Parabolic Problems, vol. 208, Pitman Research Notes Series Pitman, New York, 1989
Y. Konishi, Semi-linear Poisson’s equations, Proc. Japan Acad. 49, 100–105 (1973)
C. B. Morrey., Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966
J. A. Shercliff, Magnetic shaping of molten metal columns, Proc. Roy. Soc. London Ser. A. 375, 455–473 (1981)
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Article copyright:
© Copyright 1991
American Mathematical Society
