A mixed problem with integral condition for the hyperbolic equation

被引：31

作者：

Pul'kina, LS ^{[1
]}

机构：

[1] Samara State Univ, Samara 443086, Russia

来源：

MATHEMATICAL NOTES | 2003年 / 74卷 / 3-4期

关键词：

hyperbolic equation; Cauchy problem; Neumann boundary condition; nonlocal integral condition; Galerkin method;

D O I：

10.1023/A:1026167021195

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a mixed problem for the hyperbolic equation with a boundary Neumann condition and a nonlocal integral condition. We justify the assertion that there exists a unique generalized solution of the problem under consideration. The proof of uniqueness is based on an estimate, derived a priori, in the function space introduced in the paper, while the existence of a generalized solution is proved by the Galerkin method.

引用

页码：411 / 421

页数：11