A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

Previous Article
The initial-boundary value problem on a strip for the equation of time-like extremal surfaces
DCDS Home
This Issue
Next Article
Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters

January & February 2009, 23(1&2): 399-414. doi: 10.3934/dcds.2009.23.399

A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

1.	Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, United States
2.	Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received December 2007 Revised August 2008 Published September 2008

Abstract
Related Papers

In this paper, we study the exact controllability of a system of two weakly coupled one-dimensional wave equations with the control acted on only one equation. Using the non harmonic analysis, we establish the weak observability inequalities, which depend on the ratio of the wave propagation speeds. The obtained results are optimal.

Keywords: exact controllability, weak observability, Ingham's inequality, non harmonic analysis.

Mathematics Subject Classification: Primary: 93B07; Secondary: 93B05.

Citation: Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399

[1]	Chun Zong, Gen Qi Xu. Observability and controllability analysis of blood flow network. Mathematical Control & Related Fields, 2014, 4 (4) : 521-554. doi: 10.3934/mcrf.2014.4.521
[2]	S. S. Krigman. Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain. Conference Publications, 2007, 2007 (Special) : 590-601. doi: 10.3934/proc.2007.2007.590
[3]	Tatsien Li, Bopeng Rao, Zhiqiang Wang. Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 243-257. doi: 10.3934/dcds.2010.28.243
[4]	C E Yarman, B Yazıcı. A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group. Inverse Problems & Imaging, 2007, 1 (3) : 457-479. doi: 10.3934/ipi.2007.1.457
[5]	Lingyang Liu, Xu Liu. Controllability and observability of some coupled stochastic parabolic systems. Mathematical Control & Related Fields, 2018, 8 (3&4) : 829-854. doi: 10.3934/mcrf.2018037
[6]	Belhassen Dehman, Jean-Pierre Raymond. Exact controllability for the Lamé system. Mathematical Control & Related Fields, 2015, 5 (4) : 743-760. doi: 10.3934/mcrf.2015.5.743
[7]	Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial & Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485
[8]	Mohammed Aassila. Exact boundary controllability of a coupled system. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 665-672. doi: 10.3934/dcds.2000.6.665
[9]	Daniele Cassani, Bernhard Ruf, Cristina Tarsi. On the capacity approach to non-attainability of Hardy's inequality in $\mathbb{R}^N$. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 245-250. doi: 10.3934/dcdss.2019017
[10]	Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42.
[11]	Scott W. Hansen, Andrei A. Lyashenko. Exact controllability of a beam in an incompressible inviscid fluid. Discrete & Continuous Dynamical Systems - A, 1997, 3 (1) : 59-78. doi: 10.3934/dcds.1997.3.59
[12]	Tatsien Li, Zhiqiang Wang. A note on the exact controllability for nonautonomous hyperbolic systems. Communications on Pure & Applied Analysis, 2007, 6 (1) : 229-235. doi: 10.3934/cpaa.2007.6.229
[13]	Jamel Ben Amara, Hedi Bouzidi. Exact boundary controllability for the Boussinesq equation with variable coefficients. Evolution Equations & Control Theory, 2018, 7 (3) : 403-415. doi: 10.3934/eect.2018020
[14]	Klaus-Jochen Engel, Marjeta Kramar FijavŽ. Exact and positive controllability of boundary control systems. Networks & Heterogeneous Media, 2017, 12 (2) : 319-337. doi: 10.3934/nhm.2017014
[15]	Sara Monsurrò, Carmen Perugia. Homogenization and exact controllability for problems with imperfect interface. Networks & Heterogeneous Media, 2019, 14 (2) : 411-444. doi: 10.3934/nhm.2019017
[16]	José R. Quintero, Alex M. Montes. On the exact controllability and the stabilization for the Benney-Luke equation. Mathematical Control & Related Fields, 2019, 0 (0) : 0-0. doi: 10.3934/mcrf.2019039
[17]	Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119
[18]	S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279
[19]	S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
[20]	Ahmet Sahiner, Gulden Kapusuz, Nurullah Yilmaz. A new smoothing approach to exact penalty functions for inequality constrained optimization problems. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 161-173. doi: 10.3934/naco.2016006

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences