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On the stability of shock waves in layered structures at the presence of the electric current
Author(s):
A.
M.
Blokhin;
R.
E.
Semenko
Journal:
Quart. Appl. Math.
67
(2009),
441-475.
MSC (2000):
Primary 35Q30, 83C22
Posted:
May 6, 2009
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Additional information
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:
-
- 1.
- 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.
- 2.
- 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
- 3.
- 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).
- 4.
- 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).
- 5.
- 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).
- 6.
- 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).
- 7.
- Kats E.N., Lebedev V.V. Dynamics of liquid crystals. Moscow, Nauka, 1988 (Russian).
- 8.
- Landau L.D., Lifshits E.M. Theoretical physics. v. VII. Theory of elasticity. Moscow, Nauka, 1987 (Russian). MR 912888 (88m:00005)
- 9.
- Landau L.D., Lifshits E.M. Theoretical physics. v. VI. Hydrodynamics. Moscow, Nauka, 1986 (Russian). MR 850480 (87j:76001)
- 10.
- 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)
- 11.
- 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)
- 12.
- Sedov L.N. Mechanics of continua, v.1. Moscow., Nauka, 1970 (Russian).
- 13.
- Ovsyannikov L.V. Lectures on the foundations of the gas dynamics. Moscow, Nauka, 1981 (Russian). MR 665918 (84f:76041)
- 14.
- 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)
- 15.
- Blokhin A.M. Energy integrals and their applications to gas dynamics problems. Nauka, Sibirsk. Otdel., Novosibirsk, 1986 (Russian). MR 888816 (88m:76049)
- 16.
- Blokhin A.M. The elements of the theory of hyperbolic systems and equations. Novosibirsk. Gos. Univ., Novosibirsk, 1995 (Russian).
- 17.
- Godunov S.K. Equations of mathematical physics. Nauka, Moscow, 1979 (Russian). MR 548574 (80i:35001)
- 18.
- Bellman R. Introduction to matrix analysis. McGraw-Hill Book Company, Inc., New York, 1960. MR 0122820 (23:A153)
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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
PII:
S0033-569X-09-01155-4
Keywords:
Layered structures,
anisotropic dielectrics,
electrohydrodynamical approximaton,
linear problem,
shock waves.
Received by editor(s):
February 12, 2008
Posted:
May 6, 2009
Copyright of article:
Copyright
2009,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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