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150416t20142014riu ob 000 0 eng d |
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|a E7B
|b eng
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|c E7B
|d OCLCO
|d COO
|d EBLCP
|d DEBSZ
|d OCLCQ
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| 019 |
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|a 906578689
|a 922981907
|a 1003830029
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| 020 |
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|a 9781470420307
|q (e-book)
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|a 1470420309
|q (e-book)
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|a 1470409836
|q (alk. paper)
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|a 9781470409838
|q (alk. paper)
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| 020 |
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|z 9781470409838
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| 035 |
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|a (OCoLC)908072119
|z (OCoLC)906578689
|z (OCoLC)922981907
|z (OCoLC)1003830029
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| 050 |
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|a QA614.83
|b .D456 2014eb
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|a HCDD
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1 |
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|a Delort, Jean-Marc,
|d 1961-
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PCjJ3rxpjKMmrvF8kKxx4FX
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1 |
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|a Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres /
|c J.-M. Delort.
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| 264 |
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|a Providence, Rhode Island :
|b American Mathematical Society,
|c 2014.
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|c ©2014
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| 300 |
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|a 1 online resource (92 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
1 |
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|a Memoirs of the American Mathematical Society,
|x 1947-6221 ;
|v Volume 234, Number 1103 (third of 5 numbers)
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| 504 |
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|a Includes bibliographical references.
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|a Print version record.
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|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
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|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.
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|a Hamiltonian systems.
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|a Klein-Gordon equation.
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|a Wave equation.
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|a Sphere.
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|a spheres (geometric figures)
|2 aat
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|a Hamiltonian systems
|2 fast
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|a Klein-Gordon equation
|2 fast
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| 650 |
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|a Sphere
|2 fast
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| 650 |
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|a Wave equation
|2 fast
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| 758 |
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|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
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| 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
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| 830 |
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0 |
|a Memoirs of the American Mathematical Society ;
|v Volume 234, no. 1103 (third of 5 numbers)
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| 856 |
4 |
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|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=3114321
|y Click for online access
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| 903 |
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|a EBC-AC
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| 994 |
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|a 92
|b HCD
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