The second initial-boundary value problem for a $B$-hyperbolic equation

K. B. Sabitov ; N. V. Zaitseva

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 75-86.

Résumé

We investigate an initial-boundary value problem in a rectangular domain for a hyperbolic equation with Bessel operator. The solution is obtained in the form of the Fourier–Bessel series. The uniqueness of solution of the problem is established by means of the method of integral identities. At the existence of the proof we use assessment of coefficients of series, the asymptotic formula for Bessel function and asymptotic formula for eigenvalues. We obtain sufficient conditions on the functions defining initial data of the problem and prove the stability theorem for the solution of the problem.

Détail

Keywords: hyperbolic equation, Bessel differential operator, initial-boundary value problem, uniqueness, Fourier–Bessel series, stability.
Mots-clés : existence, uniform convergence

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