Exact controllability for a wave equation with fixed boundary control

被引：0

作者：

Lizhi Cui

Libo Song

机构：

[1] Jilin University of Finance and Economics,College of Applied Mathematics

[2] Northeast Normal University,School of Mathematics and Statistics

[3] Jilin University of Finance and Economics,Educational Administration

来源：

Boundary Value Problems | / 2014卷

关键词：

exact controllability; non-cylindrical domain; wave equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper addresses the 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 one moving. When the speed of the moving endpoint is less than 1−21+e2, by the Hilbert Uniqueness Method, the exact controllability of this equation is established. Also, the explicit dependence of the controllability time on the speed of the moving endpoint is given.

引用

共 10 条

[1]

Milla Miranda M(1996)Exact controllability for the wave equation in domains with variable boundary Rev. Mat. Univ. Complut. Madr 9 435-457

[2]

Bardos C(1981)Control and stabilization for the wave equation. Part III: domain with moving boundary SIAM J. Control Optim 19 123-138

[3]

Chen G(2004)Exact controllability for the semilinear string equation in the non cylindrical domains Control Cybern 33 237-257

[4]

Araruna FD(2013)Exact controllability for a one-dimensional wave equation in non-cylindrical domains J. Math. Anal. Appl 402 612-625

[5]

Antunes GO(1995)HUM and the wave equation with variable coefficients Asymptot. Anal 11 317-341

[6]

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