Geodesic
The second initial-boundary value problem for a $B$-hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 75-86

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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.
Keywords: hyperbolic equation, Bessel differential operator, initial-boundary value problem, uniqueness, Fourier–Bessel series, stability.
Mots-clés : existence, uniform convergence 
@article{IVM_2019_10_a7,
     author = {K. B. Sabitov and N. V. Zaitseva},
     title = {The second initial-boundary value problem for a $B$-hyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--86},
     publisher = {mathdoc},
     number = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_10_a7/}
}
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K. B. Sabitov; N. V. Zaitseva. The second initial-boundary value problem for a $B$-hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 75-86. http://geodesic.mathdoc.fr/item/IVM_2019_10_a7/