Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order

• Date: 2000
• Main Authors: Mitropolskiy, Yu. A., Khoma, N. H., Khoma, S. G., Митропольський, Ю. О., Хома, H. Г., Хома, С. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4492
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

On the basis of the exact solution of the linear Dirichlet problem \(u_{tt} - u_{xx} = f\left( {x,t} \right)\) , \(u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,\) \(0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \...