Null controllability of a parabolic equation involving the Grushin operator in some multi-dimensional domains

被引：3

作者：

Cung The Anh ^{[1
]}

Vu Manh Toi ^{[2
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

[2] Hanoi Water Resources Univ, Fac Comp Sci & Engn, Hanoi, Vietnam

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 93卷

关键词：

Null controllability; Grushin operator; Carleman inequality; HUM method; Multi-dimensional domain; APPROXIMATE CONTROLLABILITY;

D O I：

10.1016/j.na.2013.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the null controllability of the linear parabolic equation involving the Grushin operator G(s) = Delta(x) + vertical bar x vertical bar(2s) Delta(y) (s > 0), in the domain Omega = (-1, 1)(N1) x (0, 1)(N2) subset of R-N1 x R-N2, N-1, N-2 >= 1, under an additive control supported in an open subset omega of Omega. We prove that the equation is null controllable in any positive time for s < 1 and not null controllable for s > 1. When s = 1, a positive minimal time is required for null controllability. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：181 / 196

页数：16

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[2]

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