A time-step approximation scheme for a viscous version of the Vlasov equation
Analysis of PDEs
2016-12-20 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1612.06281,
title = {A time-step approximation scheme for a viscous version of the Vlasov equation},
author = {Ugo Bessi},
journal= {arXiv preprint arXiv:1612.06281},
year = {2016}
}