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

Abstract | References | Similar Articles | Additional Information

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.

**1.**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.**2.**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****3.**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).**4.**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).**5.**Kats E.N., Lebedev V.V. Liquid crystal dynamics. Moscow., Nauka, 1988 (Russian).**6.**Landau L.D., Lifshits E.M. Theoretical physics. v. VII. Theory of elasticity. Moscow, Nauka, 1987 (Russian). MR**912888 (88m:00005)****7.**Landau L.D., Lifshits E.M. Theoretical physics. v. VI. Hydrodynamics. Moscow, Nauka, 1986 (Russian). MR**850480 (87j:76001)****8.**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)****9.**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)****10.**Sedov L.N. Mechanics of continua, v.1. Moscow, Nauka, 1970 (Russian).**11.**Bogolyubov N.N., Mitropolskiy Yu.A. Asymptotic methods in the theory of the nonlinear oscillations. Moscow, Nauka, 1974 (Russian). MR**0374550 (51:10750)**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC (2000):
35Q30,
83C22

Retrieve articles in all journals with MSC (2000): 35Q30, 83C22

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

DOI:
https://doi.org/10.1090/S0033-569X-2011-01225-7

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.