Approximate controllability of the viscous Burgers equation on the real line

被引：8
|
作者：
Shirikyan, Armen [1 ]
机构：
[1] Univ Cergy Pontoise, Dept Math, CNRS UMR8088, 2 Ave Adolphe Chauvin, F-95302 Cergy Pontoise, France
来源：
GEOMETRIC CONTROL THEORY AND SUB-RIEMANNIAN GEOMETRY | 2014年 / 4卷
关键词：
NAVIER-STOKES EQUATIONS; GLOBAL-CONTROLLABILITY;
D O I：
10.1007/978-3-319-02132-4_20
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper is devoted to studying the 1D viscous Burgers equation controlled by an external force. It is assumed that the initial state is essentially bounded, with no decay condition at infinity, and the control is a trigonometric polynomial of low degree with respect to the space variable. We construct explicitly a control space of dimension 11 that enables one to steer the system to any neighbourhood of a given final state in local topologies. The proof of this result is based on an adaptation of the Agrachev-Sarychev approach to the case of an unbounded domain.
引用
收藏
页码：351 / 370
页数：20
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