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Sibirsk. Mat. Zh., 2007, Volume 48, Number 5, Pages 1134–1141 (Mi smj1795)  

This article is cited in 5 scientific papers (total in 5 papers)

Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

R. K. Romanovskii, M. V. Mendziv

Omsk State Technical University

Abstract: Considering a plane hyperbolic system with time-periodic coefficients, we construct a version of the direct Lyapunov method with the condition on the derivative of the Lyapunov functional along the trajectories of the system which is weakened by use of periodicity of the coefficients. We exhibit an illustrative example.

Keywords: Lyapunov functional, operator of translation along characteristics.

Full text: PDF file (297 kB)
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English version:
Siberian Mathematical Journal, 2007, 48:5, 913–918

Bibliographic databases:

UDC: 517.95
Received: 20.04.2005
Revised: 06.09.2006

Citation: R. K. Romanovskii, M. V. Mendziv, “Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients”, Sibirsk. Mat. Zh., 48:5 (2007), 1134–1141; Siberian Math. J., 48:5 (2007), 913–918

Citation in format AMSBIB
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\paper Stability of solutions to the Cauchy problem for a~plane hyperbolic system with time-periodic coefficients
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Romanovskii R.K., Bel'gart L.V., “On the exponential dichotomy of solutions of the Cauchy problem for a hyperbolic system on a plane”, Differ. Equ., 46:8 (2010), 1135–1144  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Belgart L.V., “Ob odnom klasse indefinitnykh funktsionalov Lyapunova”, Omskii nauchnyi vestnik, 2010, no. 3, 11–13  elib
    3. Romanovskii R.K., Belgart L.V., “Dikhotomiya reshenii zadachi Koshi dlya pochti periodicheskoi giperbolicheskoi sistemy na ploskosti”, Dokl. Akademii nauk vysshei shkoly RF, 2010, no. 2, 14–24  elib
    4. R. K. Romanovsky, E. M. Nazaruk, “Lyapunov's direct method for linear systems of functional-differential equations in Sobolev space”, Siberian Math. J., 55:4 (2014), 696–705  mathnet  crossref  mathscinet  isi
    5. Romanovsky R.K. Nazaruk E.M., “Dichotomy of Solutions of Differential-Difference Equations in a Sobolev Space”, Dokl. Math., 91:2 (2015), 193–196  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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