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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 & Continuous Dynamical Systems, 2002, 8 (3) : 745-756. doi: 10.3934/dcds.2002.8.747
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