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On the existence of a free boundary solution of the Grad-Shafranov equation

Published online by Cambridge University Press:  13 March 2009

Nobuo Fujii
Affiliation:
Department of Control Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan
Masahide Hirai
Affiliation:
Department of Control Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan

Abstract

The existence of a non-trivial free boundary solution of the nonlinear Grad-Shafranov equation is studied. In the case of axisymmetric toroids, the existence of the solution is proved by the standard variational approach using assumptions which are not physically restrictive. Also, the existence of a cylindrically symmetric solution is proved in the case of straight cylinders with circular cross-section.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1983

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References

REFERENCES

Agmon, S., Douglis, A. & Nirenberg, L. 1959 Comm. Pure Appl. Math. 12, 623.CrossRefGoogle Scholar
Bateman, G. 1978 MHD Instabilities. MIT Press.Google Scholar
Field, J. J. & Papaloizou, J. C. B. 1977 J. Plasma Phys. 18, 347.Google Scholar
Friedman, A. 1969 Partial Differential Equations. Holt, Rinehart & Winston.Google Scholar
Heron, B. & Sermange, M. 1982 Appl. Math. Optim. 8, 351.CrossRefGoogle Scholar
Mizohata, S. 1973 The Theory of Partial Differential Equations. Cambridge University Press.Google Scholar
Morrey, C. B. 1966 Multiple Integrals, in the Calculus of Variations. Springer.CrossRefGoogle Scholar
Stampacchia, G. 1966 Équations Elliptiques du Second Ordre á Coefficients Discontinu. Les Presses de L'Université de Montréal.Google Scholar
Temam, R. 1976 Arch. Rational Mech. Anal. 60, 51.Google Scholar
Thomas, C. LL. 1979 J. Plasma Phys. 21, 177.CrossRefGoogle Scholar