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Well posedness and control of semilinear wave equationswith iterated logarithms

Published online by Cambridge University Press:  15 August 2002

Piermarco Cannarsa ,
Vilmos Komornik  and
Paola Loreti
Piermarco Cannarsa
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy; cannarsa@axp.mat.uniroma2.it.
Vilmos Komornik
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France; komornik@math.u-strasbg.fr.
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. loreti@dmmm.uniroma1.it.
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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 globalexistence for all initial data. Then we improve some former exact controllability theoremsof Imanuvilov and Zuazua.

Keywords

Wave equationsemilinear equationintegral inequality

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 37 - 56
Copyright
© EDP Sciences, SMAI, 1999

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References

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Imanuvilov, O.Yu., Boundary control of semilinear evolution equations. Russian Math. Surveys 44 (1989) 183-184.
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