ON THE CONTROLLABILITY OF THE IMPROVED BOUSSINESQ EQUATION

被引：13

作者：

Cerpa, Eduardo ^{[1
]}

Crepeau, Emmanuelle ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ Paris Saclay, CNRS, UVSQ, Lab Math, F-78035 Versailles, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 04期

关键词：

Boussinesq type equation; exact controllability; approximate controllability; spectral analysis; moving control; moment method; fixed point theorem; BONA-MAHONY EQUATION; WAVE-EQUATION; NULL CONTROLLABILITY; UNIQUE CONTINUATION;

D O I：

10.1137/16M108923X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls are considered. Under some condition on the velocity at which the control moves, exact controllability results for both linear and nonlinear improved Boussinesq equations are obtained applying the moment method and a fixed point argument.

引用

页码：3035 / 3049

页数：15

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