有周期图形上波方程的形状、速度和精确可控性

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1791

S. Avdonin, J. Edward, Y. Zhao

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引用次数: 0

摘要

在有循环的图形上证明了精确可控性。控制可以是应用于边界顶点和内部顶点的混合控制。证明方法首先应用动力学论证来证明形状可控性和速度可控性，从而解决它们相关的力矩问题。这样就能解决与精确可控性相关的力矩问题。在单一控制的情况下，无论是边界控制还是内部控制，都表明精确可控性失效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Shape, velocity, and exact controllability for the wave equation on a graph with cycle

Exact controllability is proved on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first applies a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated with exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails.

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.