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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 |
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| 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 |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (92 pages) |
| Bibliografía: | Includes bibliographical references. |
| ISBN: | 9781470420307 1470420309 1470409836 9781470409838 |
| ISSN: | 1947-6221 ; 1947-6221 |