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Hamiltonian ODEs on a space of deficient measures

Chayes, L. and Gangbo, W. and Lei, H. K (2013) Hamiltonian ODEs on a space of deficient measures. Communications in Mathematical Sciences, 11 (1). pp. 1-31. ISSN 1539-6746.

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We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained based on some dynamical considerations in the form of a condition which forbids mass to return from infinity.

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Additional Information:© 2013 International Press. Received: January 12, 2012; accepted (in revised form): April 10, 2012. Communicated by Peter Markowich. The authors would like to thank IPAM for its hospitality during the Optimal Transport Workshop (Spring '08) wherein this project was conceived. L. C. was supported in part by the NSF under the grant DMS-08 05486. W. G. was supported in part by the NSF under the grants DMS-06-00791 and DMS-0901070. H. K. L. was supported in part by the Graduate Research Fellowship Program and the Dissertation Year Fellowship Program at UCLA and by the NSF under the grants DMS-10-04735 and DMS-08-05486.
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UCLA Graduate Research Fellowship ProgramUNSPECIFIED
UCLA Dissertation Year Fellowship ProgramUNSPECIFIED
Subject Keywords:Infinite dimensional Hamiltonian, ODEs on measure spaces, Wasserstein metric
Issue or Number:1
Classification Code:AMS subject classification: 37Kxx, 49-xx, 35Qxx, 53Dxx
Record Number:CaltechAUTHORS:20130207-075328964
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Official Citation:Hamiltonian ODEs on a space of deficient measures L. Chayes, W. Gangbo, and H.K. Lei
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36803
Deposited By: Ruth Sustaita
Deposited On:08 Feb 2013 17:11
Last Modified:03 Oct 2019 04:41

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