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Izvestiya: Mathematics, 2015, Volume 79, Issue 6, Pages 1260–1293
DOI: https://doi.org/10.1070/IM2015v079n06ABEH002780
(Mi im8194)
 

Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction

D. V. Tunitsky

Institute of Control Sciences, Russian Academy of Sciences, Moscow
References:
Abstract: This paper is devoted to systems of $n$ inhomogeneous equations of hydrodynamic type with two independent variables. Using a geometric formalism for such systems which goes back to Riemann, one can associate with every system of hydrodynamic type a vector field and a field of linear operators acting on an appropriate tangent bundle. In terms of these fields, we obtain a number of tests for inhomogeneous systems of hydrodynamic type to be decoupled into subsystems with block-triangular interaction. These tests supplement Bogoyavlenskii's well-known results on decoupling of homogeneous systems of hydrodynamic type into non-interacting subsystems.
Keywords: systems of hydrodynamic type, non-interacting subsystems, subsystems with block-triangular interaction, Nijenhuis tensor.
Received: 05.12.2013
Revised: 25.03.2015
Bibliographic databases:
Document Type: Article
UDC: 517.956+514.763.8
MSC: 35F50, 76N15
Language: English
Original paper language: Russian
Citation: D. V. Tunitsky, “Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction”, Izv. Math., 79:6 (2015), 1260–1293
Citation in format AMSBIB
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\paper Decoupling systems of hydrodynamic type into subsystems with block-triangular interaction
\jour Izv. Math.
\yr 2015
\vol 79
\issue 6
\pages 1260--1293
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Linking options:
  • https://www.mathnet.ru/eng/im8194
  • https://doi.org/10.1070/IM2015v079n06ABEH002780
  • https://www.mathnet.ru/eng/im/v79/i6/p171
  • Citing articles in Google Scholar: Russian citations, English citations
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    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:503
    Russian version PDF:223
    English version PDF:22
    References:83
    First page:17
     
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