Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Biccari, Umberto¹  Zuazua, Enrique² 

[1] BCAM Basque Ctr Appl Math, Alameda Mazarredo 14, Bilbao 48009, Basque Country, Spain

[2] Univ Autonoma Madrid, Dept Matemat, Campus Cantoblanco, E-28049 Madrid, Spain

关键词: Heat equation;    Singular potential;    Null controllability;    Carleman estimates;   

DOI  :  10.1016/j.jde.2016.05.019

来源: Elsevier

【 摘 要 】

This article is devoted to the analysis of control properties for a heat equation with a singular potential mu/delta(2), defined on a bounded C-2 domain Omega subset of R-N, where 3 is the distance to the boundary function. More precisely, we show that for any mu <= 1/4 the system is exactly null controllable using a distributed control located in any open subset of Omega, while for mu > 1/4 there is no way of preventing the solutions of the equation from blowing-up. The result is obtained applying a new Carleman estimate. (C) 2016 Elsevier Inc, All rights reserved.

【 授权许可】

Free