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The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation. (English. Ukrainian original) Zbl 1516.35570

J. Math. Sci., New York 227, No. 1, 68-80 (2017); translation from Ukr. Mat. Visn. 14, No. 1, 86-102 (2017).
Summary: The solvability of the problem for a nonhomogeneous partial differential equation of the second order in time and, generally, of the infinite order in the spatial variables with local conditions two-point in time in the classes of entire functions is studied. In the case of unique solvability of the problem, a differential-symbol method of construction of its unique solution is proposed. In the case of nonunique solvability of the problem, we construct a partial solution.

MSC:

35R50 PDEs of infinite order
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