On the characteristic billiard and statements of the uniqueness problem of solution to the dirichlet problem for the vibrating string equation in a domain

被引：0

作者：

Burskii V.P. ^{[1
]}

机构：

[1] Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, Donetsk

来源：

Journal of Mathematical Sciences | 2011年 / 173卷 / 2期

关键词：

Dirichlet Problem; Periodic Point; Discrete Dynamical System; Homogeneous Dirichlet Problem; Dynamical System Behavior;

D O I：

10.1007/s10958-011-0239-4

中图分类号：

学科分类号：

摘要：

The paper proposes a statement of the uniqueness problem of solution to the Dirichlet problem for the vibrating string equation in an unbounded domain containing vertical and/or horizontal strips that is convex with respect to families of characteristics of the vibrating string equation. The author proves a sufficient condition for the uniqueness of solution to the Dirichlet problem in the new statement based on the behavior of the F. John mapping realizing the characteristic billiard. Also, the author discusses the complex characteristic billiard and the statement of the uniqueness problem of solution to the Dirichlet problem for the vibrating string equation corresponding to it. © 2011 Springer Science+Business Media, Inc.

引用

页码：181 / 187

页数：6

共 19 条

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