Generalized initial-boundary problem for the wave equation with mixed derivative

We study an initial-boundary problem for a second-order inhomogeneous hyperbolic equation in half-strip of the plane containing mixed derivative with constant coefficients and zero or nonzero potential. This is transverse oscillations moving finite string. The case initial velocity fixed ends (Dirichlet conditions) considered. It assumed that roots characteristic are simple lie on real axis opposite sides origin. classical solution determined. In potential, uniqueness theorem formulated formula given form series consisting contour integrals data problem. Based this formula, concepts generalized value introduced. main theorems formulas homogeneous problems formulated. To prove these theorems, we apply approach uses theory divergent sense Euler, proposed by A.P. Khromov (axiomatic approach). Using approach, basis solutions series, proved. Further, as application obtained, existence presence summable potential give exponentially convergent series.