科研之友
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摘要
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%26apos;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 %26quot;elementary%26quot; proof.
- 出版日期2014-12-1
