New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Khodja, Farid Ammar¹  Benabdallah, Assia²  Gonzalez-Burgos, Manuel³  de Teresa, Luz⁴ 

[1] Univ Franche Comte, Lab Math Besancon, UMR 6623, 16 Route Gray, F-25030 Besancon, France

[2] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, F-13453 Marseille, France

[3] Univ Seville, Dept EDAN, Aptdo 1160, E-41080 Seville, Spain

[4] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

关键词: Parabolic systems;    Control;    Minimal time;    Geometrical dependence;   

DOI  :  10.1016/j.jmaa.2016.06.058

来源: Elsevier

【 摘 要 】

We consider the null controllability problem for two coupled parabolic equations with a space-depending coupling term. We analyze both boundary and distributed null controllability. In each case, we exhibit a minimal time of control, that is to say, a time To is an element of [0, infinity] such that the corresponding system is null controllable at any time T > T-0 and is not if T < T-0. In the distributed case, this minimal time depends on the relative position of the control interval and the support of the coupling term. We also prove that, for a fixed control interval and a time tau(0) E [0, infinity], there exist coupling terms such that the associated minimal time is tau(0). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free