Global Correctness Theorem to the Mixed Problem for a Homogeneous Two-Velocity Model Telegraph Equation with Non-Characteristic Time-Dependent Oblique Derivatives at the Ends of a String

We have proved the global correctness theorem to new mixed problem for two-velocity homogeneous model telegraph equation with non-characteristic time-dependent oblique derivatives at the ends of string. An explicit recurrent formula for a unique and stable classic solutions with a correctness criterion for mixed problem in the set of twice continuously differentiable functions are derived. Its correctness criterion consists of necessary and sufficient four matching conditions and three smoothness requirements on the initial and boundary data of non-characteristic mixed problem. These results are obtained by author’s ”method of auxiliary mixed problems for wave equations on a half-line” and ”implicit characteristic method”.