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

Biccari U, Zuazua E (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Journal of Differential Equations Elsevier

Book Volume: 261

Pages Range: 2809-2853

Journal Issue: 5

DOI: 10.1016/j.jde.2016.05.019

Abstract

This article is devoted to the analysis of control properties for a heat equation with a singular potential μ/δ2, defined on a bounded C2 domain Ω⊂RN, where δ is the distance to the boundary function. More precisely, we show that for any μ≤1/4 the system is exactly null controllable using a distributed control located in any open subset of Ω, while for μ>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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Basque Center of Applied Mathematics (BCAM) ES Spain (ES) Universidad Autónoma de Madrid (UAM) ES Spain (ES)

How to cite

APA:

Biccari, U., & Zuazua, E. (2016). Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function. Journal of Differential Equations, 261(5), 2809-2853. https://dx.doi.org/10.1016/j.jde.2016.05.019

MLA:

Biccari, Umberto, and Enrique Zuazua. "Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function." Journal of Differential Equations 261.5 (2016): 2809-2853.

BibTeX: Download