Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

被引：25

作者：

Biccari, Umberto ^{[1
,2
]}

Hernandez-Santamaria, Victor ^{[1
,2
]}

机构：

[1] Univ Deusto, DeustoTech, Bilbao 48007, Basque Country, Spain

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

来源：

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2019年 / 36卷 / 04期

基金：

欧洲研究理事会;

关键词：

fractional Laplacian; fractional heat equation; controllability; penalized HUM; PARABOLIC EQUATIONS; REGULARITY; DIFFUSION; BOUNDARY; APPROXIMATION; LAPLACIAN; SYSTEMS; POWERS;

D O I：

10.1093/imamci/dny025

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We analyse the controllability problem for a one-dimensional heat equation involving the fractional Laplacian (-d(x)(2))(s) on the interval (-1, 1). Using classical results and techniques, we show that, acting from an open subset omega subset of (-1, 1), the problem is null-controllable for s > 1/2 and that for s <= 1/2 we only have approximate controllability. Moreover, we deal with the numerical computation of the control employing the penalized Hilbert Uniqueness Method and a finite element scheme for the approximation of the solution to the corresponding elliptic equation. We present several experiments confirming the expected controllability properties.

引用

页码：1199 / 1235

页数：37

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