Russian Mathematics

, Volume 63, Issue 10, pp 66–76

# The Second Initial-Boundary Value Problem for a B-hyperbolic Equation

• K. B. Sabitov
• N. V. Zaitseva
Article

## Abstract

For a hyperbolic equation with a Bessel operator in a rectangular domain, we study the initial-boundary value problem in dependence of the numeric parameter that enters in the operator. We represent the solution as the Fourier-Bessel series. Using the method of integral identities, we prove the uniqueness of the problem solution. For proving the existence of the solution, we use estimates of coefficients of the series and the system of eigenfunctions; we establish them on the base of asymptotic formulas for the Bessel function and its zeros. We state sufficient conditions with respect to the initial conditions that guarantee the convergence of the constructed series in the class of regular solutions. We prove the theorem on the stability of the solution to the stated problem.

## Key words

hyperbolic equation Bessel operator initial-boundary value problem uniqueness existence Fourier Bessel series uniform convergence stability

## Notes

### Funding

This work was supported by the Regional Scientific and Educational Mathematical Center of Kazan (Volga Region) Federal University, project no. 0212/02.12.10179.001.

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