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
收藏
页码：1027 / 1041
页数：15
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