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

  • N. H. Khoma
  • L. G. Khoma

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.
Published
25.02.1999
How to Cite
KhomaN. H., and KhomaL. G. “A Linear Periodic Boundary-Value Problem for a Second-Order Hyperbolic Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 2, Feb. 1999, pp. 281–284, https://umj.imath.kiev.ua/index.php/umj/article/view/4611.
Section
Short communications