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This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations,...
We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position of a localized source , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation to the exact solution . By using semigroup theory, we prove existence and uniqueness...
In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.
We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set . We have chosen the tree structure with the dynamics that leads to one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number...
In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
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