On a smooth solution of a boundary-value problem

• Date: 1998
• Main Authors: Tsynalko, P. V., Цинайко, П. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4849
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study a periodic boundary-value problem for the quasilinear equation u tt −u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.