On the distributional solution of the inverse problem induced by the heat kernel method.
On the domination of a random walk on a discrete cylinder by random interlacements.
On the exact solution of a generalized Pólya process.
On the Hopfield algorithm. Foundations and examples.
On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions
The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...
On the Lax-Phillips scattering theory for transport equation
On the modified Enskog equation for elastic and inelastic collisions. Models with spin
On the motion of a body in thermal equilibrium immersed in a perfect gas
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness assumptions, the approach...
On the number of solutions of some integral equations arising in radiative transfer.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
On the Periodic Lorentz Gas and the Lorentz Kinetic Equation
We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence to the linear Boltzmann equation was proved by Gallavotti [Phys. Rev. (2)185, 308 (1969)]. The arguments presented here complete the analysis in [Golse-Wennberg, M2AN Modél. Math. et Anal. Numér.34, 1151 (2000)], where the impossibility of a kinetic...
On the spatially homogeneous Boltzmann equation
On the stationary Boltzmann equation
For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of with given indata and diffuse reflection on the boundary.
On the transient and recurrent parts of a quantum Markov semigroup
We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.
On the Transport-Diffusion Algorithm and Its Applications to the NavierStokes Equations.
On three problems of neutron transport theory
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...
On two quantum versions of the detailed balance condition
Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form (s ∈ [0,1]) in order...
On two-dimensional hamiltonian transport equations with Llocp coefficients
One-dimensional kinetic models of granular flows