American Institute of Mathematical Sciences

Advanced
July  1996, 2(3): 367-386. doi: 10.3934/dcds.1996.2.367

Exact controllability of the wave equation for domains with slits and for mixed boundary conditions

Arnaud Heibig 1, and  Mohand Moussaoui 2,

1. 

Ecole Normale Supérieure de Lyon, 46 allée d'Italie, UMPA-UMR 128, 69364 Lyon, Cedex 07, France
2. 

Ecole Centrale de Lyon, UM 5585 CNRS, BP 163, 69131 Ecully Cedex, France

Received  April 1996 Published  May 1996

We discuss the problem of exact controllability for the wave equation in a plane domain with cracks and for mixed bonudary conditions. We use the Hilbert Uniqueness Method of J.-L. Lions. We recover some results due to P. Grisvard under some less restrictive geometrical hypotheses on the domain.
Keywords: exact controllability, Hilbert uniqueness method., wave equation.
Mathematics Subject Classification: 35Jx.
Citation: Arnaud Heibig, Mohand Moussaoui. Exact controllability of the wave equation for domains with slits and for mixed boundary conditions. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 367-386. doi: 10.3934/dcds.1996.2.367
[1]

Irena Lasiecka, Roberto Triggiani. Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument. Conference Publications, 2005, 2005 (Special) : 556-565. doi: 10.3934/proc.2005.2005.556
[2]

Patrick Martinez, Judith Vancostenoble. Exact controllability in "arbitrarily short time" of the semilinear wave equation. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 901-924. doi: 10.3934/dcds.2003.9.901
[3]

Abdelmouhcene Sengouga. Exact boundary observability and controllability of the wave equation in an interval with two moving endpoints. Evolution Equations & Control Theory, 2020, 9 (1) : 1-25. doi: 10.3934/eect.2020014
[4]

Umberto De Maio, Akamabadath K. Nandakumaran, Carmen Perugia. Exact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition. Evolution Equations & Control Theory, 2015, 4 (3) : 325-346. doi: 10.3934/eect.2015.4.325
[5]

José R. Quintero, Alex M. Montes. On the exact controllability and the stabilization for the Benney-Luke equation. Mathematical Control & Related Fields, 2020, 10 (2) : 275-304. doi: 10.3934/mcrf.2019039
[6]

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
[7]

Mo Chen, Lionel Rosier. Exact controllability of the linear Zakharov-Kuznetsov equation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3889-3916. doi: 10.3934/dcdsb.2020080
[8]

Ali Wehbe, Marwa Koumaiha, Layla Toufaily. Boundary observability and exact controllability of strongly coupled wave equations. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021091
[9]

Peng Gao. Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation. Evolution Equations & Control Theory, 2020, 9 (1) : 181-191. doi: 10.3934/eect.2020002
[10]

Bopeng Rao, Laila Toufayli, Ali Wehbe. Stability and controllability of a wave equation with dynamical boundary control. Mathematical Control & Related Fields, 2015, 5 (2) : 305-320. doi: 10.3934/mcrf.2015.5.305
[11]

Mohamed Ouzahra. Controllability of the semilinear wave equation governed by a multiplicative control. Evolution Equations & Control Theory, 2019, 8 (4) : 669-686. doi: 10.3934/eect.2019039
[12]

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
[13]

Ning-An Lai, Jinglei Zhao. Potential well and exact boundary controllability for radial semilinear wave equations on Schwarzschild spacetime. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1317-1325. doi: 10.3934/cpaa.2014.13.1317
[14]

José R. Quintero, Alex M. Montes. Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021021
[15]

Lijun Zhang, Peiying Yuan, Jingli Fu, Chaudry Masood Khalique. Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2927-2939. doi: 10.3934/dcdss.2020214
[16]

Mohammed Aassila. Exact boundary controllability of a coupled system. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 665-672. doi: 10.3934/dcds.2000.6.665
[17]

Manuel González-Burgos, Sergio Guerrero, Jean Pierre Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Communications on Pure & Applied Analysis, 2009, 8 (1) : 311-333. doi: 10.3934/cpaa.2009.8.311
[18]

Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations & Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1
[19]

Umberto Biccari, Mahamadi Warma. Null-controllability properties of a fractional wave equation with a memory term. Evolution Equations & Control Theory, 2020, 9 (2) : 399-430. doi: 10.3934/eect.2020011
[20]

Michael Renardy. A backward uniqueness result for the wave equation with absorbing boundary conditions. Evolution Equations & Control Theory, 2015, 4 (3) : 347-353. doi: 10.3934/eect.2015.4.347

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (58)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences