Classical solution of the initial-boundary value problem for the wave equation with mixed derivative
Journal: Contemporary Mathematics Fundamental Directions
Year: 2024

In this paper, we study the initial-boundary value problem for a second-order nonhomogeneous hyperbolic equation in a half-strip of the plane with constant coefficients, containing a mixed derivative, with zero and nonzero potentials. This equation is the equation of transverse oscillations of a moving finite string. We consider the case of fixed ends (Dirichlet conditions). We assume that the roots of the characteristic equation are simple and lie on the real axis on different sides of the orig