Initial-Boundary Value Problem for Hyperbolic Equation with Singular Coefficient and Integral Condition of Second Kind

被引：7

作者：

Sabitov K.B. ^{[1
]}

Zaitseva N.V. ^{[2
]}

机构：

[1] Sterlitamak Branch of the Bashkir State University, pr. Lenina 49, Sterlitamak, Bashkortostan

[2] N. I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, Tatarstan

来源：

Lobachevskii Journal of Mathematics | 2018年 / 39卷 / 9期

关键词：

existence; Fourier–Bessel series; hyperbolic equation; non-local integral condition; singular coefficient; stability; uniqueness;

D O I：

10.1134/S1995080218090299

中图分类号：

学科分类号：

摘要：

We research an initial-boundary value problem with integral condition of the second kind in a rectangular domain for a hyperbolic equation with singular coefficient. The solution is obtained in the form of the Fourier–Bessel series. There are proved theorems on uniqueness, existence and stability of the solution. In order to prove the existence of solution of the non-local problem we obtain sufficient conditions for the convergence of the series in terms of the initial values. © 2018, Pleiades Publishing, Ltd.

引用

页码：1419 / 1427

页数：8

共 17 条

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