On a Cauchy Type Problem for a Second Kind Degenerating Hyperbolic Equation

In this paper a higher-order Cauchy-type problem is formulated and studied for a degenerating hyperbolic equation of the second kind in the characteristic triangle. The solution to the problem is constructed and uniqueness of solution is proved. First, the general solution of the given degenerate hyperbolic equation is constructed. Then the uniqueness of the solution to the problem is proved by the nature of the equation and by the estimation of the unknown function and its high-order derivatives with respect to second argument. In proof of the theorem the method of mathematical induction, the Gaussian hypergeometric function, Euler's gamma function, Pochhammer's symbol are used.