WSEAS Transactions on Communications
Print ISSN: 1109-2742, E-ISSN: 2224-2864
Volume 24, 2025
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
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Abstract: 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”.
Keywords:
Non-characteristic oblique derivative, method of auxiliary mixed problems, implicit characteristics
method, global correctness theorem, Hadamard’s correctness criterion
Pages: 31-43
DOI: 10.37394/23204.2025.24.6