An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Bressan, Alberto | en_US |
| dc.contributor.author | Fonte, Massimo | en_US |
| dc.contributor.department | Functional Analysis and Applications | en_US |
| dc.date.accessioned | 2005 | en_US |
| dc.date.accessioned | 2011-09-07T20:27:45Z | |
| dc.date.available | 2005 | en_US |
| dc.date.available | 2011-09-07T20:27:45Z | |
| dc.date.issued | 2005 | en_US |
| dc.description.abstract | In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result. | en_US |
| dc.format.extent | 261370 bytes | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Methods Appl. Anal. 12 (2005) 191-219 | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/1719 | en_US |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | SISSA;27/2005/M | en_US |
| dc.relation.ispartofseries | arXiv.org;math.AP/0504450 | en_US |
| dc.title | An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation | en_US |
| dc.type | Preprint | en_US |