Treffer: Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
Title:
Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
Authors:
Source:
Nonlinearity (Bristol. Print). 25(9):2579-2613
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 26 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Calcul n dimensions, Many-dimensional calculations, Dispersion onde, Wave dispersion, Dispersión onda, Equation onde, Wave equation, Ecuación onda, Espace temps, Space time, Espacio tiempo, Existence solution, Existence of solution, Existencia de solución, Méthode itérative, Iterative method, Método iterativo, Non linéarité, Nonlinearity, No linealidad, Physique mathématique, Mathematical physics, Física matemática, Potentiel, Potential, Potencial, Relation dispersion, Dispersion relation, Ecuación dispersión, Régularité solution, Solution regularity, Regularidad solución, Résonance, Resonance, Resonancia, Vecteur, Vector, 35B34, 35J05, Equation dispersion, Opérateur inverse, Opérateur linéarisé, Solution quasi périodique
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Dipartimento di Matematica e Applicazioni 'R. Caccioppoli', Universita degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126, Napoli, Italy
Universite d'Avignon et des Pays de Vaucluse, Laboratoire d'Analyse non Linéaire et Géométrie (EA 2151), 84018 Avignon, France
Universite d'Avignon et des Pays de Vaucluse, Laboratoire d'Analyse non Linéaire et Géométrie (EA 2151), 84018 Avignon, France
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26341251
Database:
PASCAL Archive
Weitere Informationen
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on Td, d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11].