2019
Том 71
№ 9

# A linear periodic boundary-value problem for a second-order hyperbolic equation

Abstract

We study the boundary-value problemu tt -u xx =g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of $\frac{\pi }{q} - , \frac{{2\pi }}{{2s - 1}} -$ , and $\frac{{4\pi }}{{2s - 1}}$ -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods $T_1 = (2p - 1)\frac{\pi }{q}, T_2 = (2p - 1)\frac{{2\pi }}{{2s - 1}}$ , and $T_3 = (2p - 1)\frac{{4\pi }}{{2s - 1}}$ which characterize the classes of π-, 2π -, and 4π-periodic functions.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 2, pp 319-323.

Citation Example: Khoma L. G., Khoma N. H. A linear periodic boundary-value problem for a second-order hyperbolic equation // Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 281–284.

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