FEEDBACK STABILIZATION OF MAGNETOHYDRODYNAMIC EQUATIONS

被引：8

作者：

Lefter, Catalin-George ^{[1
,2
]}

机构：

[1] Alexandru Ioan Cuza Univ, Fac Math, Iasi 700506, Romania

[2] Romanian Acad, Iasi Branch, Inst Math Octav Mayer, Iasi 700506, Romania

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 03期

关键词：

magnetohydrodynamic equations; feedback stabilization; Carleman estimates; TANGENTIAL BOUNDARY STABILIZATION; LOCAL EXACT CONTROLLABILITY; NAVIER-STOKES EQUATIONS; WEAK SOLUTIONS;

D O I：

10.1137/070697124

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We prove the local exponential stabilizability for the magnetohydrodynamic (MHD) system in space dimension 3, with internally distributed feedback controllers. These controllers take values in a finite dimensional space which is the unstable manifold of the elliptic part of the linearized operator. The stabilization of the linear system is derived using a unique continuation property for systems of parabolic and elliptic equations as well as the equivalence between controllability and feedback stabilizability in the case of finite dimensional systems. The feedback that stabilizes the linearized system is also stabilizing the nonlinear system in a certain interpolation space.

引用

页码：963 / 983

页数：21