On the Bitsadze-Samarskij problem for hyperbolic equations (Q1901433)

The author proves the existence of a unique solution of the wave equation \(u_{xx}- u_{yy}= 0\) on the rectangle \((- 1,1)\times (- 1,1)\) satisfying Bitsadze-Samarskij type of boundary conditions (one of them is given on the abscissa \(x= r\)) for rational \(r\) and the existence of the solution for irrational \(r\). He also gives infinitely many polynomial solutions of the generalized Bitsadze-Samarskij problem on the unit circle.