First Initial-Boundary Value Problem for B-Hyperbolic Equation

Abstract

We research an first initial-boundary value problem in a rectangular domain for a hyperbolic equation with Bessel operator. The solution of the problem depends on the numeric parameter in the equation. The solution is obtained in the form of the Fourier-Bessel series. There are proved theorems on uniqueness, existence and stability of the solution. The uniqueness of solution of the problem is established by means of the method of integral identities. And at the uniqueness proof are used completeness of the eigenfunction system of the spectral problem. At the existence proof are used assessment of coefficients of series, the asymptotic formula for Bessel function and asymptotic formula for eigenvalues. Sufficient conditions on the functions defining initial data of the problem are received.