Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres / J.-M. Delort.
"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 per...
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
2015.
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| Series: | Memoirs of the American Mathematical Society ;
no. 1103. |
| Subjects: |
| Summary: | "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."--P.v. |
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| Item Description: | "Volume 234, number 1103 (third of 5 numbers), March 2015." |
| Physical Description: | 1 online resource (v, 80 pages) |
| Bibliography: | Includes bibliographical references (pages 79-80) |
| ISBN: | 9781470420307 1470420309 |
| ISSN: | 0065-9266 ; |
| DOI: | 10.1090/memo/1103 |
| Source of Description, Etc. Note: | Description based on print version record. |