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 πq−,2π2s−1− , and 4π2s−1 -periodic functions (q and s are natural numbers). We obtain the results only for sets of periods T1=(2p−1)πq,T2=(2p−1)2π2s−1 , and T3=(2p−1)4π2s−1 which characterize the classes of π-, 2π -, and 4π-periodic functions.
Published
25.02.1999
How to Cite
Khoma, N. H., and L. G. Khoma. “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.
Issue
Section
Short communications