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


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.


Hyperbolic Equation Characteristic Problem Multidimensional Analogue Linear Hyperbolic Equation Cauchy Characteristic Problem 
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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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