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On Global Solutions for Non-Linear Hamiltonian Evolution Equations

Marsden, J. E. (1973) On Global Solutions for Non-Linear Hamiltonian Evolution Equations. Communications in Mathematical Physics, 30 (1). pp. 79-81. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20100824-113752104

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Abstract

It is shown that partial differential equations of Hamiltonian type admit global solutions in time if (a) the initial data is near equilibrium (or the coupling constant is small) (b) the linear terms have positive energy and (c) the non-linear terms are smooth functions in the topology of the linearized energy norm. The non-linear terms need not have positive energy. The result is applied to non-linear wave equations in which the interaction energy is not necessarily positive.


Item Type:Article
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http://www.cds.caltech.edu/~marsden/bib/1973/03-Ma1973/AuthorUNSPECIFIED
Additional Information:© 1973 Springer-Verlag. Received September 11, 1972. Partially supported by NSF Grant GP 15735.
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NSFGP 15735
Record Number:CaltechAUTHORS:20100824-113752104
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100824-113752104
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19634
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Sep 2010 16:27
Last Modified:26 Dec 2012 12:21

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