Hamiltonian Perturbation Theory: Separatrix Splitting, Theory and Applications

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

speaker: Ugo Bessi (Università Roma Tre)

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.

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