Electrodynamical instability of layered structures
Authors:
A. M. Blokhin and R. E. Semenko
Journal:
Quart. Appl. Math. 69 (2011), 651-676
MSC (2000):
Primary 35Q30, 83C22
DOI:
https://doi.org/10.1090/S0033-569X-2011-01225-7
Published electronically:
June 29, 2011
MathSciNet review:
2893994
Full-text PDF Free Access
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Abstract: We are concerned with a hydrodynamical model of layered structures at the presence of an electric current. We formulate a linearized stability problem for layered structures and prove that the solutions of this problem grow infinitely, which means the destruction of layered structures at the presence of the small-amplitude alternating electric current.
References
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References
- Dorovsky V.N., Dorovsky S.V. A hydrodynamic model of water-oil layered systems containing gas. Math. Comput. Modelling, 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. Modelling, 2002, v.36, pp.203-209. MR 1925071
- Gogosov V.V, Polansky V.A. Electrohydrodynamics: problem and applications, fundamental equations, discontinuous solutions. Fluid mechanics (Resume of science and technics), 1976, 10, pp.5-85 (Russian).
- Blokhin A.M., Dorovsky V.N. Problems of the mathematical simulation in theory of the multi-velocity continuum. RAS, Sib. dep, United Institute of geology, geophysics and mineralogy, Institute of Mathematics, Novosibirsk, 1994 (Russian).
- Kats E.N., Lebedev V.V. Liquid crystal dynamics. 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. Comp. and Math. with Appl., 2004, 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. Comp. and Math. with Appl., 2004, 47, pp.1379-1387. MR 2070991 (2005e:35236)
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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:
Novosibirsk State University, Novosibirsk, 630090, Russia
Email:
rsem86@mail.ru
Keywords:
Layered structures,
anisotropic dielectrics,
electrohydrodynamical approximaton,
electrodynamical instability.
Received by editor(s):
March 1, 2010
Published electronically:
June 29, 2011
Article copyright:
© Copyright 2011
Brown University
The copyright for this article reverts to public domain 28 years after publication.
