A time-step approximation scheme for a viscous version of the Vlasov equation
| Autor: | Ugo Bessi |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematics::Dynamical Systems
General Mathematics Vlasov equation Extension (predicate logic) Time step Space (mathematics) Manifold Mathematics - Analysis of PDEs Optimization and Control (math.OC) Scheme (mathematics) FOS: Mathematics 35Q83 Configuration space Mathematics - Optimization and Control Mathematics::Symplectic Geometry Analysis of PDEs (math.AP) Mathematical physics Probability measure Mathematics |
| Zdroj: | Advances in Mathematics. 266:17-83 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2014.07.023 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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