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

• Date: 1999
• Main Authors: Khoma, N. H., Khoma, L. G., Хома, H. Г., Хома, Л. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4611
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 }}...