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.

A time-step approximation for a viscous version of the Vlasov equation.

BESSI, Ugo
2014

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.
Bessi, U. (2014). A time-step approximation for a viscous version of the Vlasov equation. ADVANCES IN MATHEMATICS, 266, 17-83.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/142703
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