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Статья
2016

The method of plane waves for a hyperbolic system with several spatial variables


A. M. RomanovskayaA. M. Romanovskaya
Русская математика
https://doi.org/10.3103/S1066369X16040083
Abstract / Full Text

In the 80s of the XXth century the Riemann method for hyperbolic equations of the second order was extended to hyperbolic systems in general form with one spatial variable. In this paper, this result is extended to hyperbolic systems in general form with several spatial variables with time dependent coefficients.

Author information
  • Plekhanov Russian University of Economics, Omsk Branch, ul. 10 Let Oktyabrya str. 195, Bld. 18, Omsk, 644009, RussiaA. M. Romanovskaya
References
  1. Romanovskii, R. K. “On RiemannMatrices of the First and Second Kind”, Dokl. Akad. Nauk SSSR 267 (2), 577–580 (1982) [in Russian].
  2. Godunov, S. K. Equations ofMathematical Physics (Nauka, Moscow, 1979) [in Russian].
  3. Stein, E. M. andWeiss, G. Introduction to Harmonic Analysis in Euclidean Spaces (Mir, Moscow, 1974) [Russian translation].
  4. Egorov, Yu. V. Linear Differential Equations of Principle Type (Nauka, Moscow, 1984) [in Russian].
  5. Romanovskaya, A. M. “Stability of Solutions to Cauchy Problem for Second-Order Hyperbolic System with Periodic Coefficients”, SovietMathematics (Iz.VUZ) 31, No. 7, 56–62 (1987).
  6. Romanovskaya, A. M. The Study of Stability of Solutions to Cauchy Problem for Second-Order Hyperbolic System with Periodic Coefficients (S-print, Omsk, 2006) [in Russian].