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 [10.3934].
Viscous Aubry-Mather theory and the Vlasov equation.
BESSI, Ugo
2014-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
