Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain

被引：82

作者：

Cerpa, Eduardo ^{[3
]}

Crepeau, Emmanuelle ^{[1
,2
]}

机构：

[1] Univ Versailles St Quentin Yvelines, F-78035 Versailles, France

[2] INRIA Rocquencourt, F-78150 Le Chesnay, France

[3] Univ Paris 11, Lab Math Orsay, F-91405 Orsay, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 02期

关键词：

Controllability; Korteweg-de Vries equation; Critical domains; Power series expansion; LOCAL-CONTROLLABILITY; QUANTUM PARTICLE; POTENTIAL WELL; STABILIZATION; FLUID;

D O I：

10.1016/j.anihpc.2007.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that the linear Korteweg-de Vries (KdV) equation with homogeneous Dirichlet boundary conditions and Neumann boundary control is not controllable for some critical spatial domains. In this paper, we prove in these critical cases, that the nonlinear KdV equation is locally controllable around the origin provided that the time of control is large enough. It is done by performing a power series expansion of the solution and studying the cascade system resulting of this expansion. (c) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：457 / 475

页数：19

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