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Representation and investigation of solutions of a nonlocal boundary-value problem for a system of partial differential equations. (English. Ukrainian original) Zbl 0936.35041

Ukr. Math. J. 48, No. 2, 207-219 (1996); translation from Ukr. Mat. Zh. 48, No. 2, 184-194 (1996).
Summary: We study the boundary-value problem for a system of partial differential equations with constant coefficients with conditions nonlocal in time. By using a metric approach, we prove the well-posedness of the problem in the scale of Sobolev spaces of functions periodic in space variables. By using matrix calculus, we construct an explicit representation of a solution.

MSC:

35C05 Solutions to PDEs in closed form
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
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References:

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