Conditions for the Existence of Solutions of a Periodic Boundary-Value Problem for an Inhomogeneous Linear Hyperbolic Equation of the Second Order. I

• Date: 2005
• Main Authors: Mitropolskiy, Yu. A., Khoma-Mohyl's'ka, S. H., Митропольський, Ю. О., Хома-Могильська, С. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3653
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the periodic boundary-value problem $u_{tt} − u_{xx} = g(x, t),\; u(0, t) = u(π, t) = 0,\; u(x, t + ω) = u(x, t)$. By representing a solution of this problem in the form $u(x, t) = u^0(x, t) + ũ(x, t)$, where $u^0(x, t)$ is a solution of the corresponding homogeneous problem and $ũ(x, t)...