Ukrainian Mathematical Journal

, Volume 60, Issue 2, pp 221–234 | Cite as

Well-posedness of boundary-value problems for multidimensional hyperbolic systems

  • I. Ya. Kmit’
  • B. I. Ptashnyk


By using the method of characteristics, we investigate the well-posedness of local problems (Cauchy problem and mixed problems) and nonlocal problems (with nonseparable and integral conditions) for some multidimensional almost-linear hyperbolic systems of the first order. We reduce these problems to systems of integro-operator equations and prove theorems on the existence and uniqueness of classical solutions.


Hyperbolic System Continuous Solution Nonlocal Problem Nonlocal Boundary Condition Quasilinear Hyperbolic System 
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© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • I. Ya. Kmit’
    • 1
  • B. I. Ptashnyk
    • 1
  1. 1.Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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