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Ukrainian Mathematical Journal

, Volume 43, Issue 4, pp 379–384 | Cite as

Some boundary-value problems for linear multidimensional second-order hyperbolic equations

  • S. A. Aldashev
Brief Communications

Abstract

For the linear hyperbolic equations
$$\sum\limits_{i,j = 1}^{m + 1} {a_{ij} \left( {x,x_{m + 1} } \right)u_{x_i x_j } + \sum\limits_{i = 1}^{m + 1} {a_i \left( {x,x_{m + 1} } \right)u_{x_i } + c\left( {x,x_{m + 1} } \right)u = 0,x = \left( {x_1 ,...,x_m } \right)} ,} m \geqslant 2,$$
the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the uniqueness of a solution of the Cauchy characteristic problem is proved.

Keywords

Hyperbolic Equation Characteristic Problem Multidimensional Analogue Linear Hyperbolic Equation Cauchy Characteristic Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • S. A. Aldashev
    • 1
  1. 1.Alma-Ata Institute of Engineers of Railway TransportUSSR

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