Some controllability results for the 2D Kolmogorov equation

被引：29
作者：
Beauchard, K. [1 ]
Zuazua, E. [2 ]
机构：
[1] CNRS, ENS Cachan, CMLA, F-94230 Cachan, France
[2] BCAM, Bilbao 48009, Spain
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 05期
关键词：
Kolmogorov equation; Controllability; Carleman inequalities; NULL-CONTROLLABILITY; HEAT-EQUATION; APPROXIMATE CONTROLLABILITY;
D O I：
10.1016/j.anihpc.2008.12.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the right-hand side of the equation, located on a subdomain, that acts linearly on the state. In the first case, it is the complementary of a strip with axis x and in the second one, it is a strip with axis x. The proof relies on two ingredients. The first one is an explicit decay rate for the Fourier components of the solution in the free system. The second one is an explicit bound for the cost of the null controllability of the heat equation with potential that the Fourier components solve. This bound is derived by means of a new Carleman inequality. (C) 2009 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：1793 / 1815
页数：23
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