Null controllability for the heat equation with singular inverse-square potentials

被引：64

作者：

Vancostenoble, J. ^{[1
]}

Zuazua, E. ^{[2
,3
]}

机构：

[1] Univ Toulouse 3, CNRS, Inst Mathemat Toulouse, UMR 5219, F-31062 Toulouse, France

[2] Univ Autonoma Madrid Canto Blanco, Fac Ciencias, Dept Matemat, Madrid, Spain

[3] Univ Autonoma Madrid Canto Blanco, IMDEA Matemat, Madrid, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2008年 / 254卷 / 07期

关键词：

parabolic equation; singular inverse-square potential; null controllability; carleman estimates; observability; hardy inequalities;

D O I：

10.1016/j.jfa.2007.12.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the null controllability of the heat equation perturbed by a singular inverse-square potential arising in quantum mechanics and combustion theory. This is done within the range of subcritical coefficients of the singular potential, provided the control acts on an annular set around the singularity. Our proof uses a splitting argument on the domain, decomposition in spherical harmonics, new Carleman inequalities and refined Hardy inequalities. (c) 2008 Elsevier Inc. All rights reserved.

引用

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页码：1864 / 1902

页数：39

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