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Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres /
The Hamiltonian X([vertical line][delta]tu[vertical line]2+[vertical line][delta]u[vertical line]2+m2[vertical line]u[vertical line]2) dx, defined on functions on R x X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. We consider perturbati...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2014.
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| Colección: | Memoirs of the American Mathematical Society ;
Volume 234, no. 1103 (third of 5 numbers) |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Delort, Jean-Marc, |d 1961- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjJ3rxpjKMmrvF8kKxx4FX | |
| 245 | 1 | 0 | |a Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres / |c J.-M. Delort. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (92 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v Volume 234, Number 1103 (third of 5 numbers) | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover -- Title page -- Chapter 0. Introduction -- Chapter 1. Statement of the main theorem -- Chapter 2. Symbolic calculus -- Chapter 3. Quasi-linear Birkhoff normal forms method -- Chapter 4. Proof of the main theorem -- A. Appendix -- Bibliography -- Back Cover | |
| 520 | |a The Hamiltonian X([vertical line][delta]tu[vertical line]2+[vertical line][delta]u[vertical line]2+m2[vertical line]u[vertical line]2) dx, defined on functions on R x X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. We consider 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. We show that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size give rise to almost global solutions, i.e. solutions defined on a time interval of length cN-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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Hamiltonian systems. | |
| 650 | 0 | |a Klein-Gordon equation. | |
| 650 | 0 | |a Wave equation. | |
| 650 | 0 | |a Sphere. | |
| 650 | 6 | |a Systèmes hamiltoniens. | |
| 650 | 6 | |a Équation de Klein-Gordon. | |
| 650 | 6 | |a Équations d'onde. | |
| 650 | 6 | |a Sphère. | |
| 650 | 7 | |a spheres (geometric figures) |2 aat | |
| 650 | 7 | |a Hamiltonian systems |2 fast | |
| 650 | 7 | |a Klein-Gordon equation |2 fast | |
| 650 | 7 | |a Sphere |2 fast | |
| 650 | 7 | |a Wave equation |2 fast | |
| 758 | |i has work: |a Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH6ycm4DKyvYf38vJCb4xC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Delort, Jean-Marc, 1961- |t Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres. |d Providence, Rhode Island : American Mathematical Society, ©2014 |h v, 80 pages |k Memoirs of the American Mathematical Society ; Volume 234, Number 1103 (third of 5 numbers) |x 1947-6221 |z 9781470409838 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v Volume 234, no. 1103 (third of 5 numbers) | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114321 |z Texto completo |
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