Initial value problem for \(B\)-hyperbolic equation with integral condition of the second kind. (English. Russian original) Zbl 1395.35153
Differ. Equ. 54, No. 1, 121-133 (2018); translation from Differ. Uravn. 54, No. 1, 123-135 (2018).
Summary: For the hyperbolic equation with Bessel operator, we study the initial boundary value problem with integral nonlocal condition of the second kind in a rectangular domain. The integral identity method is used to prove the uniqueness of the solution to the posed problem. The solution is constructed as a Fourier-Bessel series. To justify the existence of the solution to the nonlocal problem, we obtain sufficient conditions to be imposed on the initial conditions to ensure the convergence of the constructed series in the class of regular solutions.
MSC:
| 35L81 | Singular hyperbolic equations |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35C10 | Series solutions to PDEs |
Keywords:
integral boundary condition; hyperbolic equation with Bessel operator; integral identity method; Fourier-Bessel seriesReferences:
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