Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat; Philippe Genta

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 5, page 939-963
  • ISSN: 0764-583X

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Cessenat, Michel, and Genta, Philippe. "Some special solutions of self similar type in MHD, obtained by a separation method of variables." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.5 (1999): 939-963. <http://eudml.org/doc/193959>.

@article{Cessenat1999,
author = {Cessenat, Michel, Genta, Philippe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {transverse component of magnetic field; MHD equations; self-similar solutions; dimensional analysis; metric separation equation; unit sphere; spherical harmonics; polarizations},
language = {eng},
number = {5},
pages = {939-963},
publisher = {Dunod},
title = {Some special solutions of self similar type in MHD, obtained by a separation method of variables},
url = {http://eudml.org/doc/193959},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Cessenat, Michel
AU - Genta, Philippe
TI - Some special solutions of self similar type in MHD, obtained by a separation method of variables
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 5
SP - 939
EP - 963
LA - eng
KW - transverse component of magnetic field; MHD equations; self-similar solutions; dimensional analysis; metric separation equation; unit sphere; spherical harmonics; polarizations
UR - http://eudml.org/doc/193959
ER -

References

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  1. [1] S. I. Braginskii, Transport Phenomena in a fully ionized two-Temperatures Plasma. Zh. Eksp. Teoret. Fiziki 33 (1957) 458-472. Zbl0085.44801
  2. [2] S. I. Braginskii, A criterion for the Applicability of the Magnetohydrodynamic Equations to a Plasma. Problems of Magneto-hydrodynamics, in Proceedings of the Conference on Magnetohydrodynamics, Riga (1958). 
  3. [3] A. B. Bud'ko, F. S. Felber, A. I. Kleev, M. A. Liberman and A. L. Velikovich, Stability analysis of dynamic Z-pinches and thetapinches. Phys. Fluids B 1 (1989) 598-607. 
  4. [4] A. B. Bud'ko, M. A. Liberman and F. F. Kamenets, Self-similar Dynamics of dense Z-pinches, AIP Conference Proceedings 195, in Dense Z-pinches, Second International Conference, Laguna Beach (1989). 
  5. [5] M. Cessenat, Mathematical Methods in electromagnetism. Linear theory and applications. Series in advances Math. 41, World Scientific (1996). Zbl0917.65099MR1409140
  6. [6] M. Cessenat and P. Genta, Une méthode de séparation des variables en magnétohydrodynamique. Rapport CEA-R-5714 (1996). 
  7. [7] R. Courant and K. O. Friedrichs, Mathematical Theory of Hyperbolic Flow Equations for Functions of two Variables. Interscience (1948). Zbl0041.11302MR29615
  8. [8] A. C. Eringen and G. A. Maugin, Electrodynamics of Continua. Springer (1990). MR1031714
  9. [9] D. S. Jones, Acoustic and Electromagnetic Waves. Clarendon Press (1986). MR943347
  10. [10] K. A. Kulikovskiy and G. A. Lyubimov, Magnetohydrodynamics. Addison-Wesley (1965). 
  11. [11] L. I. Sedov, Similarity and Dimensional Methods in Mechanics (three dimensional self similar motions of compressible media). Pergamon Press (1960). Zbl0121.18504MR108122

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