Véronique Bagland

Stationary states for the noncutoff Kac equation with a Gaussian thermostat

We study the stationary states of a Kac equation with a Gaussian thermostat in the case of a noncutoff cross section. We investigate the existence, smoothness and uniqueness of the stationary states. The theoretical results are illustrated by some numerical simulations.

Self-Similar Solutions To The Oort–Hulst–Safronov Coagulation Equation

The existence of self-similar solutions with a finite first moment is established for the Oort–Hulst–Safronov coagulation equation when the coagulation kernel is given by

Well-posedness for the spatially homogeneous Landau–Fermi–Dirac equation for hard potentials

a(y,y_*)=y^\lambda+y_*^\lambda

One-Dimensional Dissipative Boltzmann Equation: Measure Solutions, Cooling Rate, and Self-Similar Profile

for some

Moment Systems Derived from Relativistic Kinetic Equations

\lambda\in (0,1)

Equilibrium states for the Landau-Fermi-Dirac equation

. The corresponding self-similar profiles are compactly supported and have a discontinuity at the edge of their support.

Existence of self-similar profile for a kinetic annihilation model

We study the Cauchy problem for the spatially homogeneous Landau equation for Fermi–Dirac particles, in the case of hard and Maxwellian potentials. We establish existence and uniqueness of a weak solution for a large class of initial data.

Convergence of a discrete Oort–Hulst–Safronov equation

This manuscript investigates the following aspects of the one-dimensional dissipative Boltzmann equation associated to a variable hard-spheres kernel: (1) we show the optimal cooling rate of the model by a careful study of the system satisfied by the solutions moments, (2) we give existence and uniqueness of measure solutions, and (3) we prove the existence of a nontrivial self-similar profile, i.e., homogeneous cooling state, after appropriate scaling of the equation. The latter issue is based on compactness tools in the set of Borel measures. More specifically, we apply a dynamical fixed point theorem on a suitable stable set, for the model dynamics, of Borel measures.