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. https://resolver.caltech.edu/CaltechAUTHORS:20130207-075328964
|
PDF
- Published Version
See Usage Policy. 3MB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20130207-075328964
Abstract
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.
| Item Type: | Article | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| ||||||||||||||
| 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. | ||||||||||||||
| Funders: |
| ||||||||||||||
| 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 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130207-075328964 | ||||||||||||||
| 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 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||
| Deposited On: | 08 Feb 2013 17:11 | ||||||||||||||
| Last Modified: | 03 Oct 2019 04:41 |
Repository Staff Only: item control page
