Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity

被引：2

作者：

Khromov, A. P. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov 410012, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2018年 / 58卷 / 09期

关键词：

Fourier method; formal solution; wave equation; resolvent; RESOLVENT APPROACH; FOURIER METHOD; CONVERGENCE;

D O I：

10.1134/S0965542518090099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.

引用

页码：1531 / 1543

页数：13

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