American Institute of Mathematical Sciences

Advanced
July  2002, 8(3): 745-756. doi: 10.3934/dcds.2002.8.747

One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms

Piermarco Cannarsa 1, , Vilmos Komornik 2, and  Paola Loreti 3,

1. 

Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy
2. 

Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex, France
3. 

Dipartimento Metodi e Modelli Matematici, per le Scienze Applicate, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy

Received  April 2001 Revised  October 2001 Published  April 2002

In two previous works we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua on the boundary exact controllability of one-dimensional semilinear wave equations by weakening the growth assumptions on the nonlinearity. Our growth assumption is in a sense optimal. Here we adapt our method for the case of one-sided control actions. This also enables us to obtain rather general internal controllability results.
Keywords: semilinear equation, controllability., Wave equation.
Mathematics Subject Classification: 35L05, 35L70, 34A4.
Citation: Piermarco Cannarsa, Vilmos Komornik, Paola Loreti. One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 745-756. doi: 10.3934/dcds.2002.8.747
[1]

Mohamed Ouzahra. Controllability of the semilinear wave equation governed by a multiplicative control. Evolution Equations and Control Theory, 2019, 8 (4) : 669-686. doi: 10.3934/eect.2019039
[2]

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

Bopeng Rao, Laila Toufayli, Ali Wehbe. Stability and controllability of a wave equation with dynamical boundary control. Mathematical Control and Related Fields, 2015, 5 (2) : 305-320. doi: 10.3934/mcrf.2015.5.305
[4]

Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559
[5]

Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351
[6]

Martin Michálek, Dalibor Pražák, Jakub Slavík. Semilinear damped wave equation in locally uniform spaces. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1673-1695. doi: 10.3934/cpaa.2017080
[7]

Zhijian Yang, Zhiming Liu, Na Feng. Longtime behavior of the semilinear wave equation with gentle dissipation. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6557-6580. doi: 10.3934/dcds.2016084
[8]

Mohamed Ouzahra. Approximate controllability of the semilinear reaction-diffusion equation governed by a multiplicative control. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 1075-1090. doi: 10.3934/dcdsb.2021081
[9]

Abdelaziz Khoutaibi, Lahcen Maniar, Omar Oukdach. Null controllability for semilinear heat equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1525-1546. doi: 10.3934/dcdss.2022087
[10]

Umberto Biccari, Mahamadi Warma. Null-controllability properties of a fractional wave equation with a memory term. Evolution Equations and Control Theory, 2020, 9 (2) : 399-430. doi: 10.3934/eect.2020011
[11]

Arnaud Heibig, Mohand Moussaoui. Exact controllability of the wave equation for domains with slits and for mixed boundary conditions. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 367-386. doi: 10.3934/dcds.1996.2.367
[12]

Abdelmouhcene Sengouga. Exact boundary observability and controllability of the wave equation in an interval with two moving endpoints. Evolution Equations and Control Theory, 2020, 9 (1) : 1-25. doi: 10.3934/eect.2020014
[13]

Alhabib Moumni, Jawad Salhi. Exact controllability for a degenerate and singular wave equation with moving boundary. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022001
[14]

Louis Tebou. Simultaneous controllability of some uncoupled semilinear wave equations. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3721-3743. doi: 10.3934/dcds.2015.35.3721
[15]

Alfonso Castro, Benjamin Preskill. Existence of solutions for a semilinear wave equation with non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 649-658. doi: 10.3934/dcds.2010.28.649
[16]

Jiayun Lin, Kenji Nishihara, Jian Zhai. Critical exponent for the semilinear wave equation with time-dependent damping. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4307-4320. doi: 10.3934/dcds.2012.32.4307
[17]

Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603
[18]

José Caicedo, Alfonso Castro, Arturo Sanjuán. Bifurcation at infinity for a semilinear wave equation with non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 1857-1865. doi: 10.3934/dcds.2017078
[19]

José F. Caicedo, Alfonso Castro. A semilinear wave equation with smooth data and no resonance having no continuous solution. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 653-658. doi: 10.3934/dcds.2009.24.653
[20]

Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (84)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy