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Well posedness and control of semilinear wave equations with iterated logarithms

Published online by Cambridge University Press:  15 August 2002

Piermarco Cannarsa
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy; [email protected].
Vilmos Komornik
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France; [email protected].
Paola Loreti
Affiliation:
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italy. : Dipartimento MeMoMat, Università di Roma “La Sapienza”, Via A. Scarpa 16, 00161 Roma, Italy. [email protected].
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Abstract

Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 1999

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References

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