Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Published electronically: June 29, 2011
MathSciNet review: 2893994
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • 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. V. N. Dorovsky, V. S. Belonosov, and A. S. Belonosov, Numerical investigation of parametric resonance in water-oil structures containing gas, Math. Comput. Modelling 36 (2002), no. 1-2, 203–209. MR 1925071, 10.1016/S0895-7177(02)00116-4
  • 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. L. D. Landau and E. M. Lifshits, Teoreticheskaya fizika. Tom VII, 4th ed., “Nauka”, Moscow, 1987 (Russian). Teoriya uprugosti. [Theory of elasticity]; Edited by Lifshits, A. M. Kosevich and L. P. Pitaevskiĭ. MR 912888
  • 7. L. D. Landau and E. M. Lifshits, Teoreticheskaya fizika. Tom VI, 3rd ed., “Nauka”, Moscow, 1986 (Russian). Gidrodinamika. [Fluid dynamics]. MR 850480
  • 8. A. M. Blokhin and S. V. Dorovskii, Shock waves stability in layered structures, Comput. Math. Appl. 47 (2004), no. 2-3, 427–440. MR 2048194, 10.1016/S0898-1221(04)90035-1
  • 9. A. M. Blokhin, S. V. Dorovskii, and E. V. Ovechkin, Stability of shock waves in layered structures. II, Comput. Math. Appl. 47 (2004), no. 8-9, 1379–1387. MR 2070991, 10.1016/S0898-1221(04)90130-7
  • 10. Sedov L.N. Mechanics of continua, v.1. Moscow, Nauka, 1970 (Russian).
  • 11. N. N. Bogolyubov and Ju. A. Mitropol′skiĭ, Asimptoticheskie metody v teorii nelineinykh kolebanii, Izdat. “Nauka”, Moscow, 1974 (Russian). Fourth edition, revised and augmented. MR 0374550

Similar Articles

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.

Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2016 Brown University
Comments: qam-query@ams.org
AMS Website