BOUNDARY CONTROLLABILITY FOR A ONE-DIMENSIONAL HEAT EQUATION WITH A SINGULAR INVERSE-SQUARE POTENTIAL

被引：10

作者：

Biccari, Umberto ^{[1
]}

机构：

[1] Univ Deusto, Fac Ingn, Avda Univ 24, Bilbao 48007, Basque Country, Spain

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2019年 / 9卷 / 01期

基金：

欧洲研究理事会;

关键词：

Heat equation; singular potential; boundary controllability; moment method; APPROXIMATE CONTROLLABILITY; NULL CONTROLLABILITY; PARABOLIC EQUATIONS; HARDY INEQUALITIES;

D O I：

10.3934/mcrf.2019011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze controllability properties for the one-dimensional heat equation with singular inverse-square potential u(t) - u(xx) - mu/x(2)u = 0, (x, t) is an element of (0, 1) x (0, T). For any mu < 1/4, we prove that the equation is null controllable through a boundary control f is an element of H-1(0, T) acting at the singularity point x = 0. This result is obtained employing the moment method by Fattorini and Russell.

引用

页码：191 / 219

页数：29

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