In a layer obtained as the Cartesian product of an interval [−T 1 ,T 2], T 1 ,T 2 > 0, and a space ℝp , 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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 5, pp. 635–644, May, 2015.
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Kuz’, A.M., Ptashnyk, B.I. A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation. Ukr Math J 67, 723–734 (2015). https://doi.org/10.1007/s11253-015-1110-4
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DOI: https://doi.org/10.1007/s11253-015-1110-4