Well posedness and control of semilinear wave equations with iterated logarithms

Free access article

Issue		ESAIM: COCV Volume 4, 1999


Page(s)		37 - 56
DOI		10.1051/cocv:1999102

DOI: 10.1051/cocv:1999102

ESAIM: COCV, April 1999, Vol. 4, p. 37-56

Well posedness and control of semilinear wave equations with iterated logarithms

Existence, unicité et contrôle d'équations des ondes semi-linéaires avec des logarithmes itérés

Piermarco Cannarsa
Dipartimento di Matematica, Università di Roma "Tor Vergata'', Via della Ricerca Scientifica, 00133 Roma, Italy; (cannarsa@axp.mat.uniroma2.it)

Vilmos Komornik
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
Istituto per le Applicazioni del Calcolo "Mauro Picone'', Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italy. Current address: Dipartimento MeMoMat, Università di Roma "La Sapienza'', Via A. Scarpa 16, 00161 Roma, Italy. (loreti@dmmm.uniroma1.it)

Received October 5, 1998; Revised February 3, 1999;

Abstract: Motivated by a classical work of Erdos 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.

Résumé: Motivé par un travail classique d'Erdos on donne des conditions nécessaires et suffisantes de croissance de la non linéarité dans une équation des ondes semilinéaire pour l'existence des solutions globales pour toutes les données initiales. Ensuite on améliore certains théorèmes antérieurs de contrôlabilité exacte de Imanuvilov et de Zuazua.

Keywords and phrases: Wave equation, semilinear equation, integral inequality

AMS Subject Classification: 35L05, 35L70, 34A40

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