# Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres (Memoirs of the American Mathematical Society)

## J.-M. Delort

Editorial: American Mathematical Society
ISBN 10: 1470409836 / ISBN 13: 9781470409838
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Sinopsis: The Hamiltonian $\int_X(\lvert{\partial_t u}\rvert^2 + \lvert{\nabla u}\rvert^2 + \mathbf{m}^2\lvert{u}\rvert^2)\,dx$, defined on functions on $\mathbb{R}\times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of $u$. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when $X$ is the sphere, and when the mass parameter $\mathbf{m}$ is outside an exceptional subset of zero measure, smooth Cauchy data of small size $\epsilon$ give rise to almost global solutions, i.e. solutions defined on a time interval of length $c_N\epsilon^{-N}$ for any $N$. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on $u$) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.

About the Author: J.-M. Delort, Universite Paris-Nord, Villetaneuse, France.

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Título: Quasi-Linear Perturbations of Hamiltonian ...
Editorial: American Mathematical Society
Condición del libro: New

## 1.Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres (Memoirs of the American Mathematical Society; Volume 234, Number 1103)

Editorial: American Mathematical Society
ISBN 10: 1470409836 ISBN 13: 9781470409838
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Gulls Nest Books, Inc.
(Portland, OR, Estados Unidos de America)
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Descripción American Mathematical Society. Brand NEW! Paperback. Nº de ref. de la librería 438211

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## 2.Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres

Editorial: American Mathematical Society (2015)
ISBN 10: 1470409836 ISBN 13: 9781470409838
Librería
Books2Anywhere
(Fairford, GLOS, Reino Unido)
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Descripción American Mathematical Society, 2015. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9781470409838

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## 3.Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres (Paperback)

Editorial: American Mathematical Society, United States (2015)
ISBN 10: 1470409836 ISBN 13: 9781470409838
Librería
The Book Depository
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 2015. Paperback. Estado de conservación: New. Language: English . Brand New Book. The Hamiltonian $int X( lvert{ partial t u} rvert^2 + lvert{ nabla u} rvert^2 + mathbf{m}^2 lvert{u} rvert^2) ,dx$, defined on functions on $mathbb{R} times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of $u$. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when $X$ is the sphere, and when the mass parameter $mathbf{m}$ is outside an exceptional subset of zero measure, smooth Cauchy data of small size $epsilon$ give rise to almost global solutions, i.e. solutions defined on a time interval of length $c N epsilon^{-N}$ for any $N$. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on $u$) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus. Nº de ref. de la librería AAN9781470409838

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## 4.Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres (Paperback)

Editorial: American Mathematical Society, United States (2015)
ISBN 10: 1470409836 ISBN 13: 9781470409838
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 2015. Paperback. Estado de conservación: New. Language: English . Brand New Book. The Hamiltonian $int X( lvert{ partial t u} rvert^2 + lvert{ nabla u} rvert^2 + mathbf{m}^2 lvert{u} rvert^2) ,dx$, defined on functions on $mathbb{R} times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of $u$. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when $X$ is the sphere, and when the mass parameter $mathbf{m}$ is outside an exceptional subset of zero measure, smooth Cauchy data of small size $epsilon$ give rise to almost global solutions, i.e. solutions defined on a time interval of length $c N epsilon^{-N}$ for any $N$. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on $u$) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus. Nº de ref. de la librería AAN9781470409838

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## 5.QUASI-LINEAR PERTURBATIONS OF HAMILTONIAN KLEIN-GORDON EQUATIONS ON SPHERES (MEMO/234/1103)

Editorial: American Mathematical Society (2015)
ISBN 10: 1470409836 ISBN 13: 9781470409838
Librería
Herb Tandree Philosophy Books
(Stroud, GLOS, Reino Unido)
Valoración

Descripción American Mathematical Society, 2015. Paperback. Estado de conservación: NEW. 9781470409838 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0878217

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## 6.Quasi-linear Perturbations of Hamiltonian Klein-gordon Equations on Spheres

Editorial: Amer Mathematical Society (2015)
ISBN 10: 1470409836 ISBN 13: 9781470409838