Exact controllability for a one-dimensional wave equation in non-cylindrical domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Cui, Lizhi^1,2  Liu, Xu¹  Gao, Hang¹ 

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Jilin Univ Finance & Econ, Coll Appl Math, Changchun 130117, Peoples R China

关键词: Exact controllability;    Non-cylindrical domain;    Wave equation;   

DOI  :  10.1016/j.jmaa.2013.01.062

来源: Elsevier

【 摘 要 】

This paper is addressed to a study of the controllability for a one-dimensional wave equation in domains with moving boundary. This equation characterizes the motion of a string with a fixed endpoint and the other moving one. When the speed of the moving endpoint is less than the characteristic speed, by the Hilbert Uniqueness Method, the exact controllability of this equation is established. Also, an explicit dependence of the controllability time on the speed of the moving endpoint is given. Moreover, when the speed of the moving endpoint is equal to the characteristic speed, by a constructive method, we characterize a target set for the exact controllability with smooth controllers. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free