Ukrainian Mathematical Journal

, Volume 67, Issue 5, pp 723–734 | Cite as

A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation

  • A. M. Kuz’
  • B. I. Ptashnyk

In a layer obtained as the Cartesian product of an interval [−T 1 ,T 2], T 1 ,T 2 > 0, and a space ℝ p , p ≥ 1, we study a problem with nonlocal condition in the time variable containing an integral term for a mixed parabolic-hyperbolic equation in the class of functions almost periodic in the space variables. For this problem, we establish a criterion of uniqueness and sufficient conditions for the existence of solutions. To solve the problem of small denominators encountered in the construction of the solution, we use the metric approach.


Space Variable Integral Condition Integral Term Nonlocal Condition Linear Partial Differential Equation 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. M. Kuz’
    • 1
  • B. I. Ptashnyk
    • 1
  1. 1.Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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