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Ukrainian Mathematical Journal

, Volume 51, Issue 2, pp 319–323 | Cite as

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

  • L. G. Khoma
  • N. G. Khoma
Brief Communications

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.

Keywords

Periodic Solution Natural Number Classical Solution Naukova Dumka Unique Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • L. G. Khoma
    • 1
  • N. G. Khoma
    • 2
  1. 1.Ternopol Pedagogical University TernopolUkraine
  2. 2.Ternopol Academy for AgricultureTernopol

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