On the stability of shock waves in layered structures at the presence of the electric current
Authors:
A. M. Blokhin and R. E. Semenko
Journal:
Quart. Appl. Math. 67 (2009), 441-475
MSC (2000):
Primary 35Q30, 83C22
DOI:
https://doi.org/10.1090/S0033-569X-09-01155-4
Published electronically:
May 6, 2009
MathSciNet review:
2547635
Full-text PDF Free Access
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Abstract: We are concerned with a hydrodynamical model of layered structures at the presence of the electric current. We formulate a linearized stability problem for shock waves and prove its ill-posedness, which means instability of shock waves for the given model of layered structures.
References
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References
- Dorovsky V.N., Dorovsky S.V. A hydrodynamic model of water-oil layered systems containing gas. Math. Comput. Mod., 2002, v. 35, pp. 751-757.
- Dorovsky V.N., Belonosov V.S., Belonosov A.S. Numerical investigation of parametric resonance in water-oil structures containing gas. Math. Comput. Mod., 2002, v. 36, pp. 203-209. MR 1925071
- Gogosov V.V, Polansky V.A. Electrohydrodynamics: Problem and applications, fundamental equations, discontinuous solutions. Fluid mechanics (Science and technique resume), 1976, 10, pp. 5-85 (Russian).
- Dorovsky S.V., Dorovsky V.N. Possibility of electrometry at the investigation on stability of shock waves in layered structures. Geology and Geophysics, 2006, v. 47(7), pp. 892-901 (Russian).
- Dorovsky S.V., Dorovsky V.N., Blokhin A.M. Possibility of the methods of electrometry at the investigation on stability of shock waves in layered structures. Geology and Geophysics, v. 47, pp. 1185-1191 (Russian).
- Blokhin A.M., Dorovsky V.N. Problems of the mathematical simulation in theory of the multi-velocity continuum. RAS, Sib. Division., United Inst. of Geology, Geophysics and Mineralogy, Inst. of Math., Novosibirsk, 1994 (Russian).
- Kats E.N., Lebedev V.V. Dynamics of liquid crystals. Moscow, Nauka, 1988 (Russian).
- Landau L.D., Lifshits E.M. Theoretical physics. v. VII. Theory of elasticity. Moscow, Nauka, 1987 (Russian). MR 912888 (88m:00005)
- Landau L.D., Lifshits E.M. Theoretical physics. v. VI. Hydrodynamics. Moscow, Nauka, 1986 (Russian). MR 850480 (87j:76001)
- Blokhin A.M., Dorovsky S.V. Shock waves stability in layered structures. Comput. Math Appl., 2004, v. 47, pp. 427-440. MR 2048194 (2005j:35148)
- Blokhin A.M., Dorovsky S.V., Ovechkin E.V. Stability of shock waves in layered structures. Part 2. Comput. Math. Appl., 2004, v. 47, pp. 1379-1387. MR 2070991 (2005e:35236)
- Sedov L.N. Mechanics of continua, v.1. Moscow., Nauka, 1970 (Russian).
- Ovsyannikov L.V. Lectures on the foundations of the gas dynamics. Moscow, Nauka, 1981 (Russian). MR 665918 (84f:76041)
- Blokhin A.M., Merazhov I.Z., Trakhinin Yu.L. Investigation on stability of electrohydrodynamic shock waves. Le Matematiche, vol. LII (1997)-Fasc. I, pp. 87-114. MR 1624964 (99e:76125)
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Additional Information
A. M. Blokhin
Affiliation:
Institute of Mathematics, Novosibirsk State University, Novosibirsk, 630090, Russia
Email:
blokhin@math.nsc.ru
R. E. Semenko
Affiliation:
Novosibisk State University, Novosibirsk, 630090, Russia
Email:
rsem86@mail.ru
Keywords:
Layered structures,
anisotropic dielectrics,
electrohydrodynamical approximaton,
linear problem,
shock waves.
Received by editor(s):
February 12, 2008
Published electronically:
May 6, 2009
Article copyright:
© Copyright 2009
Brown University
The copyright for this article reverts to public domain 28 years after publication.