Abstract
We study a boundary-value problem with general two-point conditions with respect to the time coordinate, and periodic conditions on the spatial coordinates for Shilov-parabolic equations with constant coefficients. We construct the solution in the form of a Fourier series. We establish conditions for existence and uniqueness of a classical solution of the problem. We prove quantitative theorems on a lower bound for the small denominators that arise in solving the problem.
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Translated fromMatematichni Methody i Fiziko-mekhanichni Polya, Vol. 38, 1995.
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Zadorozhna, N.M. A boundary-value problem for parabolic equations with general nonlocal conditions. J Math Sci 81, 3029–3033 (1996). https://doi.org/10.1007/BF02362588
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DOI: https://doi.org/10.1007/BF02362588