Direct and Inverse Coefficient Problems for the Telegraph Equation with Variable Potential

For the telegraph equation with a variable potential, the solution of the initial-boundary value problem with boundary conditions of the third kind is constructed in explicit form. Then, the formulations of inverse problems for a given equation with an unknown potential and coefficients under boundary conditions are presented. Based on the spectral data of the corresponding spectral problems and on the explicit solution of the initial-boundary problem, the theorems of uniqueness and existence of solution to the formulated inverse problems are proven.