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...
Saved in:
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Online Access Connect to abstract, references, and article information e |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
2015.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1103. |
| Subjects: |
MARC
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| 100 | 1 | |a Delort, Jean-Marc, |d 1961- |e author. |0 http://id.loc.gov/authorities/names/n92066079 |1 http://isni.org/isni/0000000110840634. | |
| 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 2015. | |
| 264 | 4 | |c ©2014. | |
| 300 | |a 1 online resource (v, 80 pages) | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 234, number 1103. | |
| 504 | |a Includes bibliographical references (pages 79-80) | ||
| 500 | |a "Volume 234, number 1103 (third of 5 numbers), March 2015." | ||
| 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."--P.v. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 0 | |a Hamiltonian systems. |0 http://id.loc.gov/authorities/subjects/sh85058563. | |
| 650 | 0 | |a Klein-Gordon equation. |0 http://id.loc.gov/authorities/subjects/sh89006586. | |
| 650 | 0 | |a Wave equation. |0 http://id.loc.gov/authorities/subjects/sh85145778. | |
| 650 | 0 | |a Sphere. |0 http://id.loc.gov/authorities/subjects/sh85126590. | |
| 650 | 7 | |a Hamiltonian systems. |2 fast |0 (OCoLC)fst00950772. | |
| 650 | 7 | |a Klein-Gordon equation. |2 fast |0 (OCoLC)fst00988012. | |
| 650 | 7 | |a Sphere. |2 fast |0 (OCoLC)fst01129664. | |
| 650 | 7 | |a Wave equation. |2 fast |0 (OCoLC)fst01172869. | |
| 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, 2015 |z 9781470409838 |w (DLC) 2014041958 |w (OCoLC)893784434. |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1103. |0 http://id.loc.gov/authorities/names/n83703151. | |
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