Null controllability of some degenerate wave equations

被引：24

作者：

Zhang, Muming ^{[1
]}

Gao, Hang ^{[1
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2017年 / 30卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Controllability; degenerate wave equation; Fourier expansion; observability; STABILIZATION;

D O I：

10.1007/s11424-016-5281-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.

引用

页码：1027 / 1041

页数：15

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