Gomes and Valdinoci have introduced a time-step approximation scheme for a viscous version of Aubry-Mather theory; this scheme is a variant of that of Jordan, Kinderlehrer and Otto. Gangbo and Tudorascu have shown that the Vlasov equation can be seen as an extension of Aubry-Mather theory, in which the configuration space is the space of probability measures, i. e. the different distributions of infinitely many particles on a manifold. Putting the two things together, we show that Gomes and Valdinoci's theorem carries over to a viscous version of the Vlasov equation. In this way, we shall recover a theorem of J. Feng and T. Nguyen, but by a different and more "elementary" proof.
Bessi U (2014). A time-step approximation for a viscous version of the Vlasov equation. ADVANCES IN MATHEMATICS, 266, 17-83.
Titolo: | A time-step approximation for a viscous version of the Vlasov equation. |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Citazione: | Bessi U (2014). A time-step approximation for a viscous version of the Vlasov equation. ADVANCES IN MATHEMATICS, 266, 17-83. |
Abstract: | Gomes and Valdinoci have introduced a time-step approximation scheme for a viscous version of Aubry-Mather theory; this scheme is a variant of that of Jordan, Kinderlehrer and Otto. Gangbo and Tudorascu have shown that the Vlasov equation can be seen as an extension of Aubry-Mather theory, in which the configuration space is the space of probability measures, i. e. the different distributions of infinitely many particles on a manifold. Putting the two things together, we show that Gomes and Valdinoci's theorem carries over to a viscous version of the Vlasov equation. In this way, we shall recover a theorem of J. Feng and T. Nguyen, but by a different and more "elementary" proof. |
Handle: | http://hdl.handle.net/11590/142703 |
Appare nelle tipologie: | 1.1 Articolo in rivista |