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

被引：9
|
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.
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页码：191 / 219
页数：29
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