The Vlasov equation models a group of particles moving under a potential $V$; moreover, each particle exerts a force, of potential $W$, on the other ones. We shall suppose that these particles move on the $p$-dimensional torus $\T^p$ and that the interaction potential $W$ is smooth. We are going to perturb this equation by a Brownian motion on $\T^p$; adapting to the viscous case methods of Gangbo, Nguyen, Tudorascu and Gomes, we study the existence of periodic solutions and the asymptotics of the Hopf-Lax semigroup.
Bessi U (2014). Viscous Aubry-Mather theory and the Vlasov equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 34(2), 379-420.
Titolo: | Viscous Aubry-Mather theory and the Vlasov equation. |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Citazione: | Bessi U (2014). Viscous Aubry-Mather theory and the Vlasov equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 34(2), 379-420. |
Abstract: | The Vlasov equation models a group of particles moving under a potential $V$; moreover, each particle exerts a force, of potential $W$, on the other ones. We shall suppose that these particles move on the $p$-dimensional torus $\T^p$ and that the interaction potential $W$ is smooth. We are going to perturb this equation by a Brownian motion on $\T^p$; adapting to the viscous case methods of Gangbo, Nguyen, Tudorascu and Gomes, we study the existence of periodic solutions and the asymptotics of the Hopf-Lax semigroup. |
Handle: | http://hdl.handle.net/11590/137728 |
Appare nelle tipologie: | 1.1 Articolo in rivista |