The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous nonlinear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a m...

in this paper lie’s formalism is applied to deduce classes of solutions of a nonlinear partialdifferential equation (npde) of second order with quadratic nonlinearity. the equation has themeaning of a field equation appearing in the formulation of kinetic models. similaritysolutions and transformations are given in a most general form derived to the first time interms of reciprocal jacobian ell...

We consider the non-linear spatially homogeneous Landau equation with Maxwellian molecules in a close-to-equilibrium framework and show that the Cauchy problem for the fluctuation around the Maxwellian equilibrium distribution enjoys a Gelfand-Shilov regularizing effect in the class S 1/2 1/2(R ), implying the ultra-analyticity of both the fluctuation and its Fourier transform, for any positive...

We prove an L bound on the error made when the Wild summation for solutions of the Boltzmann equation for a gas of Maxwellian molecules is truncated at the nth stage. This gives quantitative control over the only constructive method known for solving the Boltzmann equation. As such, it has been recently applied to numerical computation, but without control on the approximation made in truncatio...

We consider a dynamical interacting particle system whose empirical distribution tends to the solution of a spatially homogeneous Boltzmann type equation, as the number of particles tends to infinity. These laws of large numbers were proved for the Maxwellian molecules by H. Tanaka ([Ta1]) and for the hard spheres by A.S. Sznitman ([Sz1]). In the present paper we investigate the corresponding l...

In this work, we model a radiofrequency discharge of hydrogenated silicon nitride in a capacitive coupled plasma reactor using Maxwellian and non-Maxwellian electron energy distribution function. The purpose is to investigate whether there is a real advantage and a significant contribution using non-Maxwellian electron energy distribution function rather than Maxwellian one for determining the ...

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characte...